The format of vehicle licence plates is pretty well described on Wikipedia at
https://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_United_KingdomBasically, two letters (originally one) were used to show a place or county, followed by up to 4 digits, such as "BC 1234". "I" or "Z" in the letters denoted places in Ireland, "S" in Scotland. There's a list in the Wikipedia article.
Some places ran out, and the order was reversed, with numbers first, starting at 1000 (1234 BC).
That became 3 letters followed by 3 digits (the original place letters with a prefix letter), such as "ABC 123". Again, as capacity was reached, the sequence was reversed, this time starting with 1 - 1 ABC.
In 1963 this was extended to have a suffix letter to show the year (ABC 123 A). Not every place had run out, so kept the old numbering, but in 1965 every car got a "C" suffix.
In 1983 the sequence was reversed - "A 123 ABC".
Some letter combinations, such as SEX, were never issued.
The scheme was changed completely in 2001.
Because the scheme was originally dealt with quite locally, the records sometimes ended up in the county archives. I know that Cheshire's early records are held in Chester. Many of the others are, as arthurk says, in the care of the Kithead Trust.
The records can be quite informative, giving details of owners and addresses.