My Muslim friends were married in a religious ceremony, but still then had to do it again in the register office for it to be recognised as a legal partnership. If he wanted (and he doesn't) he could have religious weddings with other women, but the second/third wives don't have legal standing as his wives.
Think about it, from time to time in the press we hear of British men (not Muslims, not religious) who live with a wife (or not a wife) and have children with several other women, some of whom live with him or some note. There really isn't any difference in terms of legal standing - is there?