Hello, tanya. All land in the UK is registered and whoever is named at B: Proprietorship Register in the Land Certificate is the owner. Nothing else - possession, mortgage, etc etc - has anything to do with it. Your Land Certificate is probably with whoever provided your mortgage. If you have any doubts about who actually owns your house go to www.landreg.gov.uk publications/forms then forms from the drop down menu print off Form 313 and send with �4 to your District Land Registry Office which can be found from Contact Us at the same website.
Really and truly all domestic property should be held in both names as a joint tenancy. This holds the property in equal theoretical shares, all property decisions must be made together and if one dies the property automatically and simply passes to the survivor without wills, probate, inheritance tax bills, etc. This is what you are aiming for.
If for some reason joint tenancy status is not forthcoming (it costs �40 if you do it yourself and the mortgage company will not object) then go again to forms on the website previously given and print off Form UN 1, which means unilateral notification, and send with �40 to your District Land Registry Office. This permanently blocks the registration of your property in a new name until your claim has been settled, in other words the property cannot be sold until you agree.
I have written this as if you are in England or Wales. If you are in Scotland or NI the system is the same but the form numbers are different and if you say where you are I will post contact details that will guide you through.