In terms of price, £400 will get you a decent entry-level SLR. But if you are after something small enough to fit in your pocket, you can actually spend more than you would on a budget SLR to get something with similar quality. But a Canon Powershot is a decent compact camera at a decent price.
Another option is a Bridge camera; which basically is a SLR with a non-detachable lens. They usually have super long zoom lenses but you can’t buy specialist lenses as you are stuck with the one on the camera. These are called all sorts of things, but the one below is a ‘bridge camera’, it’s the Panasonic Lumix DMC-FZ1000.
So, in no particular order here are a mix of SLRs, bridge and compact cameras; each has a link to a review on DPReview.com and a link to Wex which is a good place to buy, but Amazon and John Lewis are a couple of other places to check for prices.
Online Shop – http://www.wexphotographic.com/buy-nikon-d3300-digital-slr-with-18-55mm-vr-lens-black/p1547256
£389

Canon 100D
Review – http://www.dpreview.com/reviews/canon-eos-100d-rebel-sl1
Online Shop – http://www.wexphotographic.com/buy-canon-eos-100d-digital-slr-camera-with-18-55mm-is-stm-lens/p1536810
£369

Panasonic Lumix DMC-LX100
Review – http://www.dpreview.com/reviews/panasonic-lumix-dmc-lx100
Online Shop – http://www.wexphotographic.com/buy-panasonic-lumix-dmc-lx100-digital-camera/p1560270
£629

Panasonic Lumix DMC-FZ1000
Review – http://www.dpreview.com/reviews/panasonic-lumix-dmc-fz1000
Online Shop – http://www.wexphotographic.com/buy-panasonic-lumix-fz1000-digital-camera/p1555221
£649

Sony Cyber-shot DSC-RX100 III
Review – http://www.wexphotographic.com/buy-sony-cyber-shot-rx100-iii-digital-camera/p1553657
Online Shop – http://www.dpreview.com/reviews/sony-cybershot-dsc-rx100-m3
£639

Canon PowerShot G7 X
Review – http://www.wexphotographic.com/buy-canon-powershot-g7-x-digital-camera/p1560217
Online Shop – http://www.dpreview.com/reviews/canon-powershot-g7-x