First off, the wedding cert wont be official and valid in the UK. You will still need to do the registration here to be declared a married couple. Or if you do manage to get a marriage cert from another country, you can have it translated by a solicitor before declaring it in the UK.
From what you want, have you considered places like Cuba or Dominca? I went with my mrs to Dominica republic Puerto Plata Hotel.
You can get an all inclusive 1 week holiday in a 4/5 star hotel all inclusive for around £800-£1200 each during mid season. Let them know its your honeymoon and you mite get a free upgrade in your room.
You can simply ask the hotel to arrange a beech wedding for a few hundred pounds. Remember the USD goes a long way in those countries so the staff are always more than happy to do the extra bit for a tip.
For your budget it should be easy. Just don't arrange it here but ask the hotel to help you arrange it when you are over there and they'll get the locals to arrange the event to your requirement.