I agree that there is a potential conflict of interest. Where I have acted for couples who bought tegether in the past, and who have now split up, I will only act in this transaction where they are in absolute agreement about everything beforehand.
Any dispute, then I refuse to act for either party.
As regards costs - The op's solicitor would do the bulk of the work - take up the deeds from the bank, draft the transfer papers, complete the new mortgage documentation, conduct searches etc. The ex-girlfriend would only need a solicitor to advise her about what she's doing and witness her signature to the documents - so that fee should be a lot less, imo.