the only grounds for divorce (int he UK) are irretrievable breakdown of the marriage. Adultery may prove that it's broken down, but it's no longer grounds in itself.
I don't think the Catholic church recognises divorce (though Catholics can still get a civil divorce), but may agree to annulment of the marriage.
Make a difference to what?? Catholics don't recognise divorce you will need an annulment in order to marry again. The Catholic church does not regognise non catholic weddings either.