Frederick Haithwaite & Co. was based at 16-17 Briggate, Leeds and would almost certainly have been established in the early years of the 20th century, Mr. Haithwaite being reported as having visited both Germany and the United States to see modern methods of machine tool production. By 1918, and obviously boosted by demand during WW1, his company were trading as manufacturers, importers, agents for a number of British and overseas makers and exporters. The company's main works, at Lower Worley, had long been outgrown and - reading between the lines - it appears that many their machines were being manufactured by others, the words used saying they: " now largely control the output of four other factories". During the war, Lower Wortley had been converted to the manufacture of munitions while a second plant, the Alfred Street Works, was devoted to making aircraft fittings. Another speciality of Haithwaite was second-hand machine tools, these being rebuilt and sold from the Low Fold Mills in East Street.
A wide range of machine tools was offered with the Company's advertisements listing a range of backgeared and screwcutting lathes, mechanical hacksaws, ordinary swan-neck, multi-spindle drilling and multi-head machines and an assortment of engineering tools and accessories. However, by 1930 and the onset of the Great Depression, the Company was in difficulties and by 1934 - with plant and machinery being reported as sold off - had failed completely.
Very seldom encountered, the robustly constructed  6" x 20" backgeared and screwcutting Frederick Haithwaite lathe below must have been one of their smallest models - and was likely to have been built during the late 1920s. Of conventional design, the headstock and bed were cast as one piece - the latter being unusually wide with flat and V ways and a small (almost insignificant) gap.
Oddly, the headstock pulley was only a 2-step - so giving, with a backgear at a probable ratio of 6 :1, just four speeds, the arrangement implying that the lathe might have been intended for heavier than usual work. However, as the drive would almost certainly have come from a wall or ceiling-mounted remote countershaft, extra speeds could well have been built into that.
The spindle was supported in bronze bearings, secured with castellated adjusting nuts to set the running clearance; a ball-bearing thrust race was provided between the left-hand end of the spindle and the inner face of the left-hand bearing.
As might be expected, a proper compound slide-rest assembly was fitted, it appearing that the top slide was locked down onto the cross-slide by an inverted cone on its base - this being forced downwards by two bolts set at the front and back of the base and so giving the slide an ability to be rotated through 360°. While the cross-slide feed screw had a micrometer dial - of very small diameter - that on the top-slide did not.
Screwcutting was by ordinary changewheels, working through a tumble-reverse mechanism fitted with spring-plunger indexing. The leadscrew was of a coarse pitch - probably 4 t.p.i. - held in a detachable bracket at the tailstock end and gripped by a pair of split nuts on the apron
If you have a Haithwaite lathe, the writer would be delighted to have details and photographs.