Good question: A few years ago the British Police always had their files "open" in such cases: They were never simply "Semi-Closed" & forgotten about.
Look at the Lesley Molseed Murder: Her killer was trapped some 30 years later.
Look at the Yorkshire Ripper case & "Wearside Jack" who claimed to be the murderer but was exposed many years later as the man who wasted so much of Police Time (& arguably led to at least 2 further murders by Peter Sutcliffethe real Yorkshire ripper.)
However, as recenty as last week three UK Police Forces (sorry Police
"Services"
) are contemplating suing the Government for the swaging cuts they proposing, on the basis that they will no longer be able to simply "Police" & protect the public.
Notably, the three "Forces" involved are all in the North of the country:
Greater Manchester, Lancashire & Cumbria.And I'm pretty sure that should Merseyside Police (Liverpool area) follow suitit will leave a very large segment of the Northwest of England with a severely underfunded Police "Service".
(Thus is the North-South-Divide clearly demonstrated.)
So the anwswer to your question is simply:
"Rather depends where you live in England & Wales."