Nobody can advise you as to what is fair between a couple - that's up to you both to work out. The shares you consider fair is up to you - you could use level of contribution to the deposit as a basis of determining, or if you intend to make differeing contributions to the mortgage. Personally, unless there's going to be a major imbalance in contributions, I'd probably go 50:50. Having said that, a friend of mine went 18.75%:81.25% with his partner as she was contributing most of the money.
The thing is that you decide in advance what shares you are to have, and if you want 50:50 even though one person is contributing the entire deposit, then you can choose to take it 50:50. It's done in the deed of transfer when the property is bought, and the shares are fixed from then on.
The mortgage is slightly different - the bank will likely insist that you are jointly and severally liable for it, and it will be part of your mortgage deed. This means that if the mortgage is not paid, the bank can pursue either or both of you for the entire mortgage.