This is a great show, very unpredictable and fresh, with great acting and characterization. However, do the British police really have time and budgets to be this thorough on every cold case?
It is unclear to me whether this group is a strictly cold case unit. They are certainly going the extra mile(s) to solve this murder.
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 Sutcliffe...the 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 suit...it 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."