Well, the Marriage Certificate finally arrived but, as I feared, the space for the names of Thomas' parents is blank

The only things I have learned are that they were bachelor and spinster and his bride was Alice Janet (not Alice Jane) Davis. She was under 21 so needed her father's consent; he was Abner Davis but her mother was not named.
Unless Thomas' father's will sheds any further light I'll have to get back to searching the English records for any more clues to his earlier life.
Mike.