Railways - an excellent subject - The British Rail Class 508 (or 4PER) electric multiple-unit (EMU) passenger trains were built by BREL York works in 1979-80. They were the fourth variant of BR's standard 1972 design for suburban EMUs, eventually encompassing 755 vehicles and five classes (313/314/315/507/508). They have mostly worked on the Merseyrail network since 1983, and continue to do so, now refurbished by Alstom's Eastleigh Works.
Connex South Eastern leased twelve Class 508s freed up by capacity reductions on Merseyrail services in 1996 (508101/105/106/107/109/113/116/119/121/129/132/133), for operation on specific Kent services. Their main duties included London Bridge to Tunbridge Wells, Paddock Wood to Strood, Maidstone West to Three Bridges and Sittingbourne to Sheerness-on-Sea, as well as Grove Park to Bromley North for a short period. Units were based at Gillingham Depot. They had been refurbished at Eastleigh and renumbered 5082xx with 508 101 becoming 508 201 and 508 121 becoming 508 209
In September 2006 new operator Southeastern announced that a cascade of rolling stock would see Class 466 units replace the 508s on the Sheerness and Medway Valley lines in the December 2006 timetable. Following this timetable change the fleet was reduced to six serviceable units. There were five sets in 'warm store' at Ashford Chart Leacon, and one unit, 508212, was cannibalised to keep the surviving service units in operation, including the swap of its TSO coach with one from a unit that ran into a tree on the Redhill to Tonbridge Line. With the transfer of the Tonbridge to London via Redhill services to Southern, Southeastern placed its remaining 508s in store in December 2008. Your last two pictures show the units working for Southeeastern.
One cab each from 508201 and 508209 [ as per your pictures] went to Emergency Services Training Centre, Seacombe and were repainted in all over yellow livery
Look out for more class 507 and 508 units being withdrawn by Merseyrail as their new units take over -
https://www.railengineer.co.uk/new-merseyrail-connected-trains/