You could ask each solicitor in your town if they are the one,but I do feel they would be very reluctant to discuss a client unless you were included in the dead persons will ? Its very difficult that sort of thing. My Brother died a couple of years ago and his wife who hated me refused to tell me where or when the funeral was. Even the undertaker refused without her,the next of kins permission.
I suppose it depends on why you want to know? Even if you found the solicitor I doubt if he or she would discuss it without the permission of the next of kin ? I would try and find out from the next of kin..