Hi - this is an era that I've found really interesting so I can tell you what i've found out for the Midland in Derbyshire at least.
Re coaches
I've seen pics up until about 1953 of LMS crimson with no LMS markings, roundel and with a M before the number. From memory I think the coaches in the 'fireworks and chilcompton' train pack are these. I have a feeling the M is serif, though I'm sure I've seen pics where it's not. There might well be variations on this but I'd have to study my books.
I've seen 1 pics of a period 1 vehicle in 1951 (I think) still with the original livery, LMS and number. This maybe because it's older or just hasn't visited works for a bit.
Re locos:
Seemingly Derby and Crewe still renumbered locos with LMS on the tender. Highlights include a number of Jubilees in both Crimson and 1946 black with their Gill Sans BR numbers and smokebox plates. Also Patriots (though less) - But Beds and Herts was LMS crimson with BR gill sans number in 1950! You get '1946' Scots too. I'm no expert on the Pacifics though rails hamilton is 1946 with a BR number (though the letters on the tender are too low)
One I do like is 43000 which ran in plain black with he proper 1946 letters on the tender. Beware of smokebox plates as some were gill sans, some LMS serif. And also Compound 934 which was in Crimson until 1950 If the photo I have is correct. It has a smokebox plate of 40934 - a winner for Bachmann perhaps!
On freight engines you get similar but not with the gill sans in the photos I've seen. Derby put the number on with serif transfers. Crewe seemed to use the 1946 style font but without the outline around the numbers. The still might have serif LMS on their tenders thought. It would seem that at least the Garratts were renumbered with that no outline 1946 style font with LMS on the cab sides.
Then of course you have the liveries where they've banged an M on the front of the number. Not my favourite, but still different. There are a few crabs I've seen in the style - the smokebox plate looks very odd as they've bolted the M on the LH side...
then you get the BRITISH RAILWAYS liveries, which came in. interestingly I read that the big gap was because they thought they would put an emblem between the letters. They never did though.
I hope that gives you an idea...I've picked this stuff up from reading books about the Peak line and seeing the photos from the period. Also David Hey's collection online is great. Eric Treacy took a good number of pics from the period which I've found interesting too. Finally of course, if you want livery advice, the Essay and Jenkinson 'locos of the las series' is great. But I would say trawl for pics - there is some surprising stuff!