It is extremely unlikely that she would have any claim upon the property because (a) it was bought long after you separated, (b) it is obviously your home and that of your new partner and (c) after all this time I assume your ex already has somewhere to live and is not sleeping in shop doorways.
Having said that, you would be wise to check if you and divorced and, if not, to do something about that as soon as possible. That is because being married has all sorts of consequences apart from the one you mention. In the event of your death your wife might, for instance, have a claim upon your estate or upon any pension you may have. She could also be your next of kin for purposes of turning off your life support. You can find out if you have been divorced by conducting a search for decree absolute at the Search Section of the Central Family Court, 41 High Holborn, London WC1. This can be done by post and you can probably find more information online.