The first 15 001-015 were built theoretically for the Manchester-Wilmslow-Crewe scheme.
The next 20 016-035 were theoretically for the Liverpool-Crewe scheme. However, as only three were needed daily for this service, this was obviously inaccurate, and the bulk operated from Manchester, where 15 units were not enough.
The last 10 036-045 were for the Manchester-Stoke-Birmingham scheme, although completed well before the wiring was done. Again, they generally operated from Manchester.
The 45 units overall, however, did pretty much cover all the local services north of Birmingham, including the later incorporation of the Altrincham line. When the electrification was extended to the north in 1973 they did a once daily service from Crewe to Preston, operating via Earlestown and Newton-le-Willows, about the only electric service to do so.
The equivalent 305/308 units operating out of Liverpool Street did have a proper refurbishment in 1980, with new bogies (actually secondhand), properly draughtproofed doors, new interiors and in-unit corridor connections. They were actually quite nice, and in many respects better than new vehicles of the period. They certainly had seats far better than were being installed in 313s/507s of the period of their installation, plus they of course properly lined up with the windows. I understood the difference with the 304s was due to different standards of asbestos insulation in the different builds, and that the stock reductions of the time, most easily done by eliminating middle trailers, were also due to economising in asbestos treatment - it wasn't necessarily stripped, but in many was fully sealed in. This gave various difficulties where such vehicles were subsequently involved in accidents with the bodywork ripped open.