You say you love the location but hate the house. Is there anything at all you could do to improve the house - convert the attic. change box room into dressing room, put on extension, change the internal layout, I could go on but don't know the house.
In other words what is it specifically that you hate about the house and can this change??
You have enough in savings to cover the negative equity and the costs of solicitor for a purchase, you lack deposit. How much are you looking at spending on a next house?
I don't think you would get a new mortgage on top of what you have.