(2 part post):
There are two ways of jointly owning a property. If your parents were 'joint tenants' then neither of them owned any share of the house. It was their legal partenership (as a single entity) which owned the whole of the house. When your mother passed away your father, as the new sole member of the 'partnership', automatically became the owner of the whole house. (If, for example, your mother had left a will giving her share of the house to the Battersea Dogs' home, that provision of her will would have been totally invalid since she didn't actually own a share of the house).
Assuming that your parents were joint tenants, all that your father needs to do is to download and complete form DJP:
http://www1.landregis...ary/documents/djp.pdf
and then send it, with a copy of your mother's death certificate, to the relevant Land Registry office:
http://www1.landregistry.gov.uk/regional/