Firstof all you must do everything you can to try to find y
our ex girlfriend. Start off by asking mutual acquaintances, or what about her parents. Try 192.com. You can also try using the DSS. Thy know where everyone is (you are either paying or claiming), and although they will not tell you her address will forward a letter. This is best attempted through a solicitor.
If she is genuinely untraceable once all reasonable effeorts have been mase, apply to the court as suggested above. You definitely will need a solicitor.
The equity will be divided in the shares that you agreed when you purchased the property. The fact that you have paid the mortgage for the last eight years probably counts for nothing, as you may well have had to pay a similar sum were you to have been renting, so in effect all you have been doing is keeping a roof over your head.