Muslim weddings vary enormously according to the culture of the people involved.
Many people in the UK, for example, confuse the celebrations at a Pakistani or Bangladeshi wedding with an Islamic wedding, and assume they are the same thing. This is not so, of course, for many of the Muslims who marry are from widely different cultures - for example European, Turkish, African, Malaysian, and so on.
Secondly, it is important to realise that the 'wedding' means different things too. For many Muslims, it is the Islamic ceremony that counts as the actual wedding, and not the confirmation of that wedding in a registry office.
Oddly enough, although mosques are obviously places of worship, the majority of them in the UK have not yet been officially registered as such, and so any Islamic wedding that merely takes place at a mosque has to be registered legally with the UK law as well, in order to be seen as valid in the UK.
Having said that, of course it is a fact that many couples live together these days as 'partners', and 'common law wives' have recently been accorded various legal rights they were not entitled to previously.