Honestly, I would say that it's not worth the hassle of doing this. There are a number of very tricky complications that could come into it, I can only tell you how tricky my situation is now.

My Mum passed away in 2010. Before she died, her and my Dad were joint tenants on the property, which means that no share of the property is apportioned, and if one person dies, the property is left to the other person. However, she notified my Dad of a change to tenants in common, which apportioned the property 50% each way. This is because in the first case, you cannot leave property to anyone else other than the other property owner. This was so that she could leave her share in trust for my me and my sister. This was done and has a couple of consequences - my Dad has the ability to live in the property for however long he goes on for, and also, he cannot sell the property without both mine and my sister's written permission.

Move a few years down the line, and my Dad has met someone else (who me and my sister are both on good terms with). I'm just about to graduate, and my sister still has a few years left at University. His new partner still has a (small) mortgage, and after my sister graduates they're thinking of buying a property together. This becomes very complicated, as the terms of my mum's will only allows him to do so if my sister and I are named on the property. If they therefore wanted to take out a small mortgage on the property they are seeking to buy, there could possibly be implications in that way on me and my sister.

So, there's a few things you should think about. a) If your dad meets someone else, and she moves into the property, he has every right to say in his will that she can continue to live there after his death, if he predeceases her - or at least, she could continue to do so until it was taken to court. b) How would you divide the house if you were to go on the mortgage right now? You say you're planning to buy your mum out of it - but who is fronting the cash to do so? Or are you and your father planning to take out another mortgage divided equally? c) You mention that it's possible your Dad loses his job, but equally have you thought about your own situation? d) Have you thought about the implications of wanting to buy your own property later down the line? Some of the government house schemes are only for first time buyers, and if you have a share on a property like this, it might impact your situation wrt the current schemes and any future ones. e) Normally with a mortgage you have some kind of insurance that pays it off if someone who is a payee dies on it. This was certainly what happened when my mum passed away. You need to find out about this though.

Basically there are many many complications you've not thought about, and you need to see a solicitor, no matter how expensive. You said you're in your early twenties, and that suggests to me that you might change your mind later on about paying into this - if you need a mortgage of your own when you meet someone and want to buy a house, this could get in the way of that, no matter how you feel about it now.