If both names are on the deeds it's important that the type of joint ownership is established.
If the title register shows that your father and grandmother are 'tenants in common' they each own a share of the house. (Unless specified otherwise in the deeds, that will be 50%). Upon your grandmother's death (assuming, of course, that your father doesn't die first) her half will go to the beneficiary named in her will. (i.e. your cousin). The other half will still belong to your father, since nobody can bequeath anything in their will which they don't actually own.
If, as is possibly more likely, the title register shows that your grandmother and your father are 'joint tenants' then neither of them owns a share of the house. It's their legal partnership which owns the whole house. When one of the partners dies the surviving partner AUTOMATICALLY owns the whole of the house. i.e. when your grandmother dies your father will become the sole owner of the property. Anything in your grandmother's will relating to the disposal of the house will be totally invalid. As explained above, she doesn't own a share of the house, so she can't leave any part of the house to anyone.
You can consult the title register for the house, to find out which type of joint ownership applies, for a fee of £4 here:
https://www.landregis...ortal/Property_Search
Chris