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
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
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
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
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
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