Wills and probate
If an individual died without a will, then letters of administration would be granted permitting the heir at law or next of kin to dispose of the estate. Furthermore, from 1796, death duty was payable on the estate, and the registers often detail next of kin, as well as later annotations.
In terms of locating family members, wills are the most important of the sources you are likely to find. In England and Wales you will find separate will registers for the Prerogatives Courts of Canterbury (at The National Archives) and York (at the Borthwick Institute, York) that go up to 1858. Thereafter all English wills have been registered centrally (and copies of wills can be obtained from the Principal Probate Registry, London).
Wills registered in local diocesan courts can be found at the relevant county or diocesan record office. A separate system exists in Scotland, and its records can be found in Edinburgh. Irish wills are mainly kept in Dublin, with copies available in Belfast (although most wills prior to 1914 have been destroyed).