Modified collets and nosepiece of the Mk. 1A. Based on the Schaublin ESX design, these collets were developed with the express intention of providing a superior grip on the shanks of cutting tools.
An important part of the new assembly was a freely-floating compensating washer that fitted between the collet and nose cap; this was intended to eliminate possible inaccuracies between the locknut thread and its inner surface that clamped against the collet.

The ordinary collets of the Mk. 1. These were available in both fractional sizes and also as a 'solid' unit with a No. 5 B & S or No. 1 Morse taper shank.
In case of difficulty with collets see: collets

Above and below: for light-duty machining boring heads and drill chucks were available on plain shanks to fit into a collet. For heavier-duty work they could be supplied with a more rigid "collet" fitting for direct mounting within the spindle nose.

With a classic machine tool like the Linley it's rather fun to find and use the maker's original toolmaker-style vise (above) and high-quality rotary table (below).