I had a 'proper' (I'm assuming you mean traditional?) wedding for around £8k in total, a few years ago. We had 80 day guests and about 120 in the evening. So it's definitely doable, but you do have to think differently about some parts of it.
We found a lovely country pub that was licensed for weddings and just had a very down to earth couple in charge. They charged a hire fee of £800 (for a Saturday wedding) and then nothing else had a wedding mark up. As in, we had a roast for our wedding breakfast and they charged the same as they would on a Sunday. They also allowed us to pay corkage and provide our own wine. Incredibly lucky! It took a lot of creative googling and asking recently wedded couples for venue tips, so I'd definitely take the time to research all possible venues.
We didn't go for a lot of the 'expected' wedding elements, like fancy favours, hiring cars etc. We just had family drive us instead. Very simple table settings and simple flowers (the bridesmaid had a single flower, and my 'bouquet' was about 8 or so flowers - but the effect was stunning). All of those elements really adds up, so if cost is an issue then definitely consider which ones are really worth it.
My dress cost about £400 including alterations. Everything else - accessories, bridesmaid dresses, groomsman outfits etc - were high street. All looked amazing.
We were offered a lot of services by friends or family for free, which again was very lucky. So our stationery, photos, cake all cost us nothing (we obviously arranged lovely gifts as thank yous!).
You can do your own/each others hair, make up etc.
One of the most fun part of the planning for us was the music.. We did our own play list and provided our own sound system (the pub had disco lights etc). Itasnt as polished, but it was so personalised, and we had all of our guests choose a song on their rsvp. It went down amazingly well.
As I say, I know we were very lucky in many ways with ours. We didn't miss a single thing we didn't go for (like cars, fancy table settings etc), and everyone after commented on just how relaxed and fun the day was. Hopefully some of these tips will prove helpful to you! Good luck and enjoy the planning!