Contrary to popular belief, there is no such thing as a legal separation. You are either married or divorced . (Judicial separation is the same process as a divorce ie taking about 6 months and is only appropriate for people with a religious objection to divorce. If you later decided to divorce, you would then have to repeat the process only this time with a petition for divrorce rather than a petition of judicial spearation.)
But as far as the buikding soicety is concerned, they have no interest in whether you are married or divorced or living apart. Their only concern is to avoid risk to themselves. Obviously, with 2 names on the mortgage deed, the building society has less risk than if only one person is named, because both people are jointly and severally lible for the whole of the nortgage, rather than just one.
It is possible to transfer ownership of a property into one person's sole name even while the mortgage remains in joint names, so if your husband was agreeable, you could do that - but his own solicitor might advise him not to agree, on the basis of why should he keep the risk of being named on the mortgage deed, without also the benefit of being a joint owner.
In a divorce case, the house would not be considered in isolation, but the court court would look at a fair dvision of all the matrimonial assets ie everything in your name, everything in his name (including savings and pensions) and everything owned jointly. So, depending on the financial circumstances of both of you, the court could order a lump sum payment from your husband to you, to reduce the mortgage to a level you could afford, and the transfer of the house into your sole name. In return, you might agree not to make a cliam aginst his pension.
I hope this helps and I wish you the best of luck.
Thanks and best wishes...