Your best bet is to work back through the Probate Service.
When someone dies, their representative invariably has to apply for a Grant of Representation. There are 3 types of grant - probate (when the Will appoints an executor), Letters of Administration (when there was a Will but the grant is made to someone not an executor) and LoA (when there was no Will).
I suppose there could be a few people with no possessions where none of these 3 are applied for - but in virtually every case, the Probate Service will have some record.
To get a Grant of Representation the original Will HAS to be given to the probate registrar who keeps it. A copy appears on both the grant issued and file records in the probate service.
If a Will was filed with a solicitor (and it could only be the original, or it would be pointless exercise), someone must have withdrawn it to get the necessary Grant of Rep.
You can get the Probate Service to do a search for a fee, or DIY for free. You need basic information like the full name and last address and date of death - otherwise it will be a needle-in-a-haystick job.
See here
http://www.hmcourts-service.gov.uk/cms/1226.htm#howdoi