Manufactured during the late 1940s and early 1950s by Barker Machine Tools & Equipment Ltd. of 156 Fulham Palace Road, London W6 and registered under "Provisional Patent" No. 2209-47, the 5" x 24" (and 5" x 36") Barker was an unusual lathe that employed three bed bars to provided a stiff  "box-section" mounting for the carriage - in principle, if not appearance, rather like a Rivett 608. The bars socketed into cast-iron housings at each end of the "bed" with that on the left forming a heavy base upon which the headstock was arranged to swivel in a way that allowed taper threads to be cut without a taper-turning attachment - and tapered shafts, bores and flanges to be machined under power. The headstock spindle ran in a pair of Timken taper-roller bearings (with chucks mounted on a Hardinge-like quick-lock taper nose) whilst a bevel gear under the centre of the headstock transmitted a drive out to a conventional changewheel arrangement.
To simplify the problem of fixing a drive system to a swivelling headstock, and to make the machine as compact as possible, the electric motor was bolted directly to the headstock cover plate and drove down through 2-step V pulleys (with the belt tensioned by a jockey wheel) to pick-off gears that provided a range of high and low speeds. The high range (driven from the larger motor pulley at a ratio of 2 : 1) were: 100, 165, 250, 370, 564, 710 and 912 low and low range (from the pulleys at 3 : 1):  66, 110, 169, 246, 375, 475 and 610 rpm. The three slowest speeds in each range were achieved by an additional backgear system built into the headstock. These were useful ranges for what might be considered a rather eccentric design of lathe but could only by obtained by the laborious and inconvenient means of swapping around, in various combinations, 8 oily gears. Like the screwcutting changewheels, the spindle drive was guarded by a large, swing-open  cast-aluminium cover - but neither (in line with the relaxed safety rules of the day), had any form of safety locking mechanism.
Screwcutting was by ordinary changewheels with a set of 17 being supplied to generate all the common English threads from 2 to 60 t.p.i. Power for the sliding and surfacing feeds was taken from a keyway in the leadscrew which, in the absence of tumble reverse caused by the unusual headstock design, was equipped with a "reversing gearbox" at its headstock end similar in design to that fitted to the American Atlas 10-inch lathe. Both feeds were selected and engaged by a single 3-position lever on the front face of the apron. A small plate riveted to the lathe instructed the operator how to use the automatic release for the sliding feed: "Use reverse box lever as a dead stop . Traverse lever will then disengage easily".
As standard a typically English style T-slotted cross slide was supplied (that mirrored the bed design by running on two bars) with sliding sheet metal covers to protect the feed screw from swarf and dirt. Strangely - for at the time every ordinary industrial-class lathe was provided with one - a separate swivelling top slide available only as an extra - the lathe below, obviously not fitted with one when new, has been equipped by a previous owner with what looks like the slide from a Holbrook. 
The No. 2 Morse set-over taper tailstock was designed with a usefully exaggerated "lean forward" for the barrel that allowed drills and other fitting to reach right up to the spindle nose.
It is believed that the lathe was always supplied ex-works fitted to a strong sheet-steel cabinet stand with two large storage cupboards and a deep chip tray.
The one Barker to pass through the writer's hands had suffered a hard life but with the restoration of slideway adjustments, the replacement of the upper front bed bar and a little fettling, it proved surprisingly accurate and capable of taking a decent cut..