The court on divorce can order the transfer of the tenancy in to your name. You apply for the order on form Form D50B (see here www.gov.uk/government/publications/form-d50b-application-under-s17-of-the-married-womens-property-act-1882-s66-of-the-civil-partnership-act-2004-application-to-transfer-a-property ).
There should be a statement in support. The statement should confirm your eligibility to apply, that the tenancy is a relevant tenancy, and that one or both of the parties, as the case may be, is entitled to occupy the property by reason of the tenancy. The criteria on which the court will exercise its discretion should also be addressed. They are:
In determining whether to exercise its powers under Part II of this Schedule and, if so, in what manner, the court shall have regard to all the circumstances of the case including—
(a)the circumstances in which the tenancy was granted to either or both of the spouses /civil partners or cohabitants or, as the case requires, the circumstances in which either or both of them became tenant under the tenancy;
(b)the matters mentioned in section 33(6)(a), (b) and (c) and, where the parties are cohabitants and only one of them is entitled to occupy the dwelling-house by virtue of the relevant tenancy, the further matters mentioned in section 36(6)(e), (f), (g) and (h); and
(c)the suitability of the parties as tenants
s33(6) says:
(e)the housing needs and housing resources of each of the parties and of any relevant child;
(f)the financial resources of each of the parties;
(g)the likely effect of any order, or of any decision by the court not to exercise its powers on the health, safety or well-being of the parties and of any relevant child; and
(h)the conduct of the parties in relation to each other and otherwise.
s36(6) deals with the situation when the parties have not been married, so not relevant to you.
If there are other assets, eg pensions or an income such that you may have a realistic claim for spouse maintenance you should also apply for a financial remedy order on Form A.
You should issue the application in the same court that the divorce is in.
There is a court fee of £245 but if your income is low you may be exempt.