Can you re-write the question? To explain it better?
Like this.
I'm separating, I own a house jointly, mortgage free, with my wife.
(this is what I think you're saying). She wants to buy me out and give me 50% of the value. She needs to get a mortgage from the bank to do this. She can/cannot afford the mortgage on her own
If that is what you're asking then you really do need to be talking to solicitors. Are there any children? Are there other assets? Where are you going to live?
At the very least, you both need solicitors for the conveyancing.
mf