Hi
If you've swapped using
http://swapmysim.o2.co.ukTry turning your phone off and on to reset it or turn airplane mode on and off.
If that does not help and service has stopped on your old SIM card which indicated the swap has started then leave it a short while, turning airplane mode on and off every 30 minutes and maybe contact O2 Customer Services to check all is ok ,and it's just not the network being busy that's delaying the swap.
http://www.o2.co.uk/contactusIt could also be a faulty SIM card.
Any O2 high street shop can perform the swapmysim for you too ,or ask customer service to post out another.
Let us now how you get on please.