The outstanding loan would appear to explain exclusion from the mortgage - I agree with Sheena1's read on it, that your being on the mortgage could reduce the total borrowings you'll be eligible for as a couple. However, I think you need sound legal advice on the specific issue of excluding you from the deeds, as any future transfer of part of the property to you, save only (I think) in the case of marriage, could carry tax implications. Likewise, if you, once earning, are contributing to the mortgage without having your name on mortgage and deeds, your position in establishing any right in the property (as you'll be aware, no doubt) in the case of break-up will be difficult and costly to prove.
I can't, frankly, see any way that you can be taken into account for TRS if you aren't on the mortgage or the deeds, so you'll have to work on the basis of only one buyer - unless you can find a lender prepared to be more flexible.
Good luck with it!