Almost certainly made in Germany by Ehrlich - a large manufacturer of conventional lathes - lathes branded as IXL were first factored in the UK early in the 20th century by Pittler (represented by George Adams in London, who had strong German connections) and then by Tyzack and J.G.Graves. The latter two were companies with very large mail-order businesses, Tyzack tending towards machine-tool sales but J.G.Graves (of Sheffield) having a very much wider and more general product spread.
Besides examples marked "Leader" (both with and without additional IXL markings), some IXL lathes have the prefix "BEC", standing for "B. Elliott Co.", once the largest UK machine-tool agents who, it is believed, may have had some designs constructed for them by Ransomes, Sims & Jefferies. However, the connection to Elliott is tenuous, for the appearance of IXL in catalogues of various independent tool dealers does not make sense - Elliott having their own distribution system and non of their (many other) machine tools are known to have been sold in this way. It is also possible that some versions of the IXL may have been constructed under a sub-contract agreement with the well-known Britannia company. One trick practised in the past (before it was made illegal) was to put "British Made" or "Made in England" on some easily detached part such as a changewheel cover or stand door; while the marked part might indeed have been cast in the United Kingdom, the rest of the lathe was an import. The same trick was practised by sellers of wallets with a little tab marked "Real Leather". You've guessed it - the tab might have been leather, the rest was a cheap imitation. However. whatever the truth of the matter as to the maker, lathes branded as IXL seem to have enjoyed buoyant sales and today appear regularly on auction sites and for-sale lists.
A mainstay of the range for many years was the 6-inch x 40" V-bed Model A.K.T., a machine sometimes found on a heavy treadle-powered stand but more usually with the optional "fast-and-loose" countershaft unit--the illustration of which below was taken from the "Graves" mail-order catalogue. Interestingly, this lathe was fitted with an apron mechanism to provide both power sliding and surfacing but, on the cheaper versions, only the power surfacing, operated from a push-pull knob on the face of the apron, was connected up. However, if the owners had realised it, they could have quickly rigged up a simple cam arrangement, operated by a rod passing through the already-drill second hole, and enjoyed a leadscrew-independent power sliding feed as well. The A.K.T. was also available in a "light" version, the Model "A". Although the two lathes appear to have been almost identical they were, in almost every respect, different with the Model A having, for example, a shorter headstock (11.125" against 13 inches), shorter but slightly larger diameter spindle bearings; smaller-diameter  headstock pulleys, a smaller leadscrew (although at 1-inch it was only 1/8" less in diameter) and a tailstock shorter by 3/4-inch. However, one fitting on the "A" missing from the A.K.T. (and a useful recognition point) was T-slotted saddle wings (though of course, to confuse matters, this fitting is also occasionally found on other models). The writer has had several IXL lathes of various sizes pass through his hands and, though sold as a relatively inexpensive machine, all were made from good quality materials with an excellent finish. Detail touches included the leadscrew hanger bearings being properly doweled to the bed and castellated adjustment nuts used liberally wherever backlash had to be eliminated.
Today the most common IXL lathe seems to be the "Leader", a backgeared and screwcutting machine with a capacity of 5" x 24" that went through a steady evolution during its life. Many IXL lathes were available with a range of specifications including beds of various lengths with and without gaps, different stands and several kinds of countershaft - as well as the usual types of accessory. The smaller IXL lathes, of around 5" centre height, were also marketed by Tyzack using the Zyto name - and sometimes a confusion of names as well, with both Zyto and IXL names cast into different parts of individual machines. If you have an IXL of any vintage and would like to contribute to a photographic essay on the make, the writer would be pleased to hear from you.
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With a design of headstock that originated in the early years of the 20th century the gap-bed 5" x 20"  IXL Model W3  followed, in some respects, the design of the contemporary Drummond 3.50-inch "Flat bed" with the lathe going through a process of evolution where the Mk. 1 had its leadscrew running down the centre of the bed with a geared handle on the end for manual traverse of the carriage. On the Mk. 2 the leadscrew was moved to a conventional position of the front of the bed and the carriage fitted with a handwheel (carried on a bracket bolted to the right-hand face of the apron) that engaged directly with a bed-mounted rack. Unfortunately, the arrangement produced a high-geared arrangement, where a small turn of the handwheel produced an awkwardly-large movement of the carriage. Finally, on the Mk. 3, the apron was completely redesigned and fitted with a train of reduction gears between handwheel and rack that gave a much finer rate of feed - and hence greater control to the operator. The top of the bed was flat, with V-edges, and fitted as standard with an open gap able to accommodate a piece of metal 15.5-inches in diameter and around 3 inches thick on the faceplate.
Listed right into the 1930s the W3 continued to be the baby of the IXL range when, at £30 : 10s : 0d,  it was a useful £17 cheaper than the heavy-duty A.K.T. and £9 less than the lightweight version of the same machine the "61/2" Model "A". Of light construction to modern eyes (but with a stiffening bar linking the two bearings) the headstock held a 9/16-inch bore spindle running in tapered bronze bearings (that were split and adjustable for wear with large C-spanner rings) and with end thrust taken against a ball race. A 3-step flat belt cone pulley was fitted (with steps of 3.125, 4.125 and 5.125-inch diameter) driven by a treadle-powered flywheel overhung on the outside of the headstock-end leg. Although treadle-powered lathes remained popular into the 1920s (electricity was still not available in many country areas), conventional wall and ceiling-mounted countershafts with fast-and-loose pulleys were also available. A wholly unnecessary arrangement allowed the headstock casting to rotated slightly on the bed to allow tapers to be turned, but there was no dowel pin to reset its central position - this tricky job had to be done by eye against a mark scribed across the front clamping boss. A conventional sliding-engagement backgear arrangement was fitted but, to keep down the list price, guards over the gears (as on many similar small lathes in the early 1900s), were charged extra at what the makers described as a "nominal cost". Drive to the 6 t.p.i. leadscrew was though changewheels and a robust tumble-reverse mechanism; gears were secured by a neat spring-loaded bush that, when pulled, allowed a slotted washer to be slipped off and the gears changed very easily. The leadscrew was carried in hanger brackets, correctly doweled to the bed, with the left-hand assembly arranged to take thrust and adjustable for end clearance by a castellated nut. 17 properly machine-cut cast-iron changewheels were provided (including a 127 metric translation wheel) that allowed generation of all common inch thread pitches between 1/64" and 1/2-inch. Although at the time it was not unknown for very inexpensive lathes to use iron gears "as cast", on the IXL a further refinement was the use of stronger steel gears for the tumble-reverse assembly.
With  4 T-slots to allow boring and milling operations, the wide cross slide carried a single-bolt top slide that could be swivelled through 360 degrees - though the result was a less-than-rigid mounting with the tool thrust taken through a flex-inducing path to the bed. Although the swivel of the top slide was graduated, neither top nor cross slide carried micrometer dials, another failing of most contemporary small lathes.
Mounted on its treadle and flywheel stand the IXL W3 weighed around 435 lbs and was supplied as standard with an 8.625-inch diameter faceplate, a catchplate, a hand T-rest with two lengths of T, a set of changewheels and the necessary spanners..

Above and immediately below: a Mk. 3 IXL Model W3 with some modifications by the owner: a large, neatly-mounted micrometer dial on the cross slide and a dividing attachment connected through the changewheels.

The leadscrew was carried in hanger brackets, correctly doweled to the bed, with the left-hand assembly arranged to take thrust and adjustable for end clearance by a castellated nut.

IXL Mk. 2 Model W3 with the carriage traverse handwheel carried on a bracket fastened to the apron's right-hand face. The large micrometer dial is an owner's modification.

A Mk. 3 Model W3 IXL with reduction gearing to the carriage hand-traverse. Note the relatively wide cross slide and castellated adjustment nuts on both compound slide rest feed screws

Just visible in this picture is the boss at the front of the headstock that carried the second clamping bolt and the alignment line required to reset the headstock after it had been swivelled.