A UK registered cars history can be checked with the DVLA as long as it has a V5.

You need to complete Form V888 downloadable from the DVLA website and mail it off to the DVLA with a cheque for £5

What you should get back is a list of the former keepers of the vehicle plus information such as engine and colour changes from computerization (circa 1983) onwards and before if they have it!

Not sure if you need to be the registered keeper or whether an interested party can obtain the info.

Recently obtained the full registration history for my 1968 Plus 4 even though it was originally registered in London (VGK81F) and the Greater London Council destroyed all their registration records! Best 5quid I spent!