There is no statutory register of wills (prior to the death of the testator and probate being obtained) in this country.
Some people choose to register the
existence of their wills with the Law Society's endorsed provider, 'Certainty' (which is a registered charity), but that register doesn't hold the actual wills (or any copies of them); it only records the locations of will. (So, even if the will's existence was registered with Certainty, the only information they'd hold would be that it was stored in the safe).
Certainty's service is only really useful in cases where, for example, a will was stored with a solicitor's firm which has since gone out of business; the charity can then seek to trace where it might have ended up.
I have little doubt that thousands of wills simply 'disappear' every year where a person who would benefit under the intestacy laws realises that they'll do less well under the provisions of a will. (Let's be honest here. When my father died I would probably have seen to it that his will would have mysteriously 'vanished' if he hadn't left everything to me in it - and I'm far from the most dishonest person in the world!)
Where there appears to be no will (whether there ever was or not in reality), the person(s) with entitlement to inherit the estate can take control of the assets of that estate without the need to seek 'letters of administation' (which is the equivalent to a 'grant of probate' where a will exists) if the value of the estate is fairly low. You can find an indication of the maximum amounts that different banks will hand over without letters of administration (or a grant of probate) in this link here;
https://www.co-oplegalservices.co.uk/media-centre/articles-may-aug-2018/bank-limits-for-probate/
In such cases it might be hard to track down the transfer of funds, as
(a) you'd need to know the name of the relevant bank ; and
(b) they'd be bound by strict rules on confidentiality anyway.
If the deceased person co-owned a house with their spouse as 'joint tenants' (which is the most usual arrangement) then, as far as the house is concerned, the contents of the deceased person's will are completely IRRELEVANT.
If the will stated, for example, "I leave my share of the house to the Battersea Dogs' Home", that provision would be NULL AND VOID, as it's the 'partnership' between the two people that owned the WHOLE of the house (rather than each of them owning a separate half of it), with the sole surviving partner AUTOMATICALLY acquiring full title to the property upon the death of the other person. While it's advisable for the surviving partner to notify the Land Registry of the death of their spouse (so that only one name is left showing on the title register), it often doesn't happen, with the survivor simply continuing to live in the property (and with the executor/administrator of his/her estate then needing to get the records updated).
Where two people co-own a property as 'tenants in common' (with each of them owning a half share in it, which they're then free to leave to whomever thet like in their will), or where the deceased person owned the whole of the property, then (assuming that the spouse is due to inherit the other half of the property, either under the terms of a will or under the intestacy laws), it's once again not unusual for the spouse to simply carry on living in the house until, after his death, the executor/administrator of his/her estate has to sort out the paperwork.
However you can check up on who is currently registered as holding the title to the property for just £3 here:
https://eservices.landregistry.gov.uk/eservices/FindAProperty/view/QuickEnquiryInit.do