There are two key words here - "Beeching Axe"
Basically the Beeching Report of 1963 proposed the closure of pretty well all conventional rural branch line termini (Quite a few of the more minor ones had already gone - the ER had its first round of closures in 1951 ). The easy targets such as branchlines went first , and by 1968-70 they were closing main lines like the Waverley Route, the Midland Peak Forest route, the Woodhead Route (for passengers) and the remains of the GC London extension. By the end of 1970 the process had basically run its course (I like to be very parochial indeed and consider the closure of the E.Lincs line and associated Mablethorpe branch on 5/10/70 as effectively the end of the Axe )
Sometimes the freight ended a year or two before final closure to passengers, sometimes freight lingered a few years after closure to passengers
A few remaining branches succumbed in the next few years (1971-5) : Penrith/Keswick, the Swanage branch , the Minehead branch , the Alston branch, the Bridport branch all come to mind. Whether any of them still carried freight in their last few years I'm not sure. I don't think so - BR was heammoraging freight in the 1960s, and the classic pickup goods was rapidly vanishing
By the 1970s the limited number of surviving branches had often lost their freight and were just passenger sidings. Some did keep a little freight, but in general it wasn't found in a classic branch line terminus. EG there was freight in the 70s on the Barton on Humber branch , which is still open , but it was bglock trains from the Shellstar plant partway down the line : the terminus had been bulldozed and was just a single line to a bare platform with a bus shelter surrounded by brambles and rubble
Come to that there is still freight on the Sheringham branch - block trains from N Walsham gas terminal (sidings behind the station which retains its loop and until recently its box) and there used to be some grain from Wroxham . But Cromer hasn't seen a freight train since the 60s and Sheringham is another basic terminus - platform, brambles , length of track
Lymington surves and is electrified - but no freight , just a EMU shuttle (I think freight ended in the 60s). Braintree is also electrified and I believe retained some freight into the 80s - but the goods yard at Braintree was completely separate from the passenger station
Capt Grumps has covered Yorks in the 70s and 80s.
Perhaps more helpful is to consider how early the diesels arrived. In E. Lincolnshire , local services were in the hands of DMUs from 1955 onward - first the original Derby Lightweights, then the 114s which saw over 30 years service in the county, most of it based at LN. In 1955-62, all the local stations were still open and nearly all the branches : Spilsby, Louth/Wragby, and Horncastle had closed to passengers but still saw freight (the first 2 went completely soon after). Steam finished completely by about 1964-5, but most of the network survived, a virtually pure GN secondary railway , run entirely by diesels until late 1970
Something similar happened in E. Anglia - steam finished completely in Sept 1962, before Beeching even went to press. Lines like that to Wells next the Sea didn't close until 1969 , and even then most of that line remained for freight, being cut back steadily from Fakenham back to E Dereham during the 70s and early 80s (Though Wells was a bit bigger than the usual model BLT - E.Lynn owes a lot to Wells)
So if you model a lot of places in the early-mid 60s, you can run a traditional rural railway using some diesels or even fully dieselised. In fact it's a potentially very attractive option, buit rarely seen. Jas Millham's Yaxbury branch (in S) and Three Mills (3mm/14.2mm gauge) are fine examples set in 60s E.Anglia
Generally it was the DMUs that arrived first. The LNER didn't waste money on new engines and coaches for unremunerative branch lines (the LMS did) Consequently the ER found itself with a lot of lines worked by clapped out Edwardian tank engines
