Thank you for your quick responses.
In communications, I sent a text message at the initial stage to her. I said the options were basically, we buy each other out or sell.
I sent her a text saying (verbatim) 'If you bought me out it would need to include the deposit I put down (minus what you paid of course).'
She replied 'OK. Thanks. We'll do what we can to help each other out'.
The deposit was done so we both benefitted from a better mortgage rate. I remortgaged another property to do this and the remainder of these funds paid the stamp duty and solicitors. I calculated what the cost of this additional borrowing was and we split this. I however, paid her back what she paid towards this in the £3,750 payment I made to her to 'release' her from the property (this was itemised in a spreadsheet calculation that she constructed and we subsequently agreed to include deductions for the stamp duty and solicitors cost that I paid from the remortgage).
In our communications since there has been no discussion about the deposit. She has merely referenced benefitting from the increase in property value in the 3 months we have owned. I said this broke our original agreement and if she wanted to do this and get a valuation she would need to pay the money back I gave her as that was to 'release' her from the property (she pays nothing towards it now).
I now do want want to incur costs in view that she may not sign over the mortgage and deeds. She has recently ignored communications from me.