Advice for someone who was not married

We have a house together, probably £150,000 of equity and I want to sell. I moved out, lots of reasons but mainly because he had an affair and wouldn't go. I'm now in housing association property. I'm desperate to sell up and move on. I am currently having the mortgage coming out of my account. I am terrified he will miss payments and the house ends up being reposessed and we both end up with nothing. I have tried mediation and he chose not to engage. So the next step is a solicitor. What kind of solicitor should I engage? The last one I spoke to was not much help, did not give me any recommendations because she dealt with primarily divorces. My children are teenagers, 13 16 and 18 so too old for any formal arrangements. Can anyone help? Both our names are on the mortgage but I have paid it myself for the last two years or so. Before that it was a joint account.