Does my fiance have to be baptised to get married in a Church of England ceremony?

Some specific churches do and some don't. If the priest has not mentioned anything and it says nothing about it I would say that you will be ok to go ahead with the wedding as you have planned it. Many people these days are married in a church without being baptised, but if you are having m he will not be able to participate (though he can go up for a blessing).