OK, the death cert doesnt rule out a wife or children, they may have predeceased him, they may have not been local, or have been too upset, or 101 other reasons why they didnt register his death.
For a will, you can search the indexes free at the probate registry in Holborn London, (and also I believe at local Probate offices, so if you are nearer Leeds that might be worth pursuing).
If you find there is a Will or Letters of Administration then a copy can be sent for, at cost of £5, from the Probate place in York.
Alternatively you can just contact York and they will include a search for a year or so in the £5.
All details on -
http://www.hmcourts-service.gov.uk/cms/1226.htm