There are two ways in which two people can jointly own a house:
If your mother and her boyfriend are
'joint tenants', then it is effectively their 'partnership' (in a business sense) which owns the house (rather than them each owning half of it). If one person dies, the other person is the sole survivor of that partnership and therefore automatically becomes the sole owner of the house. (If the deceased person was to leave a will, apparently giving their 'share' of the house to someone else, that part of the will would not be valid because they never actually owned a 'share' of the house. The other partner would still get the whole house).
If your mother and her boyfriend are
'tenants in common' they both own a share of the house. (The split would normally be '50-50' but it's possible for the deeds to define a different distribution, such as '60-40' or anything else). As such, they are free to leave their share of the house to whoever they like. It could be the surviving partner or it could be Battersea Dogs' Home; it's entirely up to the individual. The surviving partner would, of course, still retain the ownership of their share of the property. (If the deceased person died without leaving a will, their share would be allocated according to the rules of intestacy. Only family members, and not boyfriends or girlfriends, can inherit under those rules)
So the first thing to do is to find out whether the property is owned as a joint tenancy or as a tenancy in common. Anyone can do that, for a fee of �3, by downloading the title register from here:
http://www.landregisteronline.gov.uk/
Chris