Hi there,
The legal requirements for marrying in the Uk can be found
here. You specifically need to check out what documentation you need to provide being a non-Brit.
Unfortunately you have to register with the Civil Registrar to marry anywhere other than the Church of England. The Church of England has some special arrangements (Common or Special licences), so we would suggest that your fiancee contacts her local Anglican priest to enquire.
Otherwise, you might have to arrange the wedding while you are over here and then return at some point. I'm not sure there are many ways that you can get round this. It is not as easy to arrange a marriage as it is in USA.
Best wishes to you both,
Kate