I'll have a go at reducing these:
Church: £200 - this'll be a fixed cost I imagine if a day and church already set
Flowers: £300 - chose simpler flowers and not so many. Or, do you have space to plant and grow flowers? I've heard of green-fingered people doing this for budget weddings, and its' been lovely. Tie them with ribbon.
Vicar: £100 - again, assume fixed cost
Dress: £800 - start shopping for bargains and consider second hand
Suits & others to dress: £3000 - don't have matchy matchy bridesmaids, maybe even just choose a colour and let them choose their own dresses. Refund them to a set amount.
Band: £500 - don't scrimp on this, they'll make the party
Photographer: £500 - hire them for only a very short collection of shots. Ask friends and family to share their pics instead. Ask close friends to make a bit of an effort to do this in case people forget.
Booze: £1000 - choose a venue where you can bring your own, go for a quick trip to France before we leave the EU and buy loads of nice booze! (I know a couple who did this)
Pre-meal snacks: £1k - You can definitely save on this. Get snacks from M&S or waitrose, don't pay caterers to do it.
Hotel for OP afterwards: £500 - this sounds like a lot! Surely this can come down.
Favours & shoes & whatever: £1k. Don't have favours. Waste of money. Do get a small gift to thank bridesmaids and ushers though
Vehicle hire: £1k - you can halve this or less, if you hire through Turo (like AirBnB for cars).
Reception Venue with buffet meal???
This one suggests £1500 minimum for 100 ppl, but let's call it £4.5k instead for OP's specific dates.
This is key. Ideally, find a pretty community venue and caterers who won't cost the earth.