Council right to buy

[pat42]

I'm just about to buy my flat under the right to buy scheme. My ex partner no longer lives with me, but to get the mortgage I've had to put in both of our names because our tenancy is in both names. She has no problem with this as long as I pay her a certain amount of money. I will register as tenants in common and state the ownership is 99% in my favour by way of a trust deed. Will this be shown to the Council's solicitors or will it just be registered as a joint purchase where no proportions of the ownership are shown?
Also, is a trust deed totally, legally binding? Cheers!