I spent less than £3000 on my wedding and I cut out nothing I really wanted.
Have a look at you local town hall, if you don't want a Register Office. If you want a church, have a look if they have a Church Hall next door. Not moving people makes the whole thing less stressful and means you aren't stressing about travel arrangements.
The thing is to decide which 'bits' will 'make' your wedding. For me it was venue, so that's where my money went - but the venue being striking (and not that expensive, see Town Hall comment) meant that I didn't need massive flowers or chair covers or whatever.
I did Rochdale Town Hall (£1300 all day exclusive, ceremony and reception) about £500 on food and another £200 on drinks. I had seventy people for my cold 'sit down' buffet at 4.30pm (3.30pm ceremony) and 110 for the evening 'pie and pea' supper.
I hired a DJ, put disposable cameras on tables and gave every set of guests a CD to put photo's on from their digital cameras.
My flowers were my bouquet, three single stem roses for my Bridesmaids and 5 buttonholes for Dh, best man, both Dad's and my brother (who gave me away). I bought silk copies for the ushers. £125.
My dress was made for me, and very non-traditional, I paid £70 for the fabric for that, plus that for bridesmaids dresses, also made.
Have a think about what's important to you and don't get sucked into wedding 'must haves' - they're just costly wastes of money. There's very little of the stationary you can't knock up on a computer, for example.