PsychoDan

Get the One Plus 3T, it has a great camera, 5.5 inch 1080p display, is pretty fast (it even has 6GB of RAM! o_0), a 3500 mAH battery and it fits well in your budget

I'd suggest the Inspiron 15 7000, it's around a $1000 so you'd be able to save some money and you can get it with a gtx 1050ti (which will be fine for 1080p gaming), an i7 7700HQ and 16gb of RAM and best of all has a battery life of 8 - 9 hours when not gaming, so is great for productivity on the go, it is 1 inch thick and has a nice build quality

I'd recommend the One Plus 3T, while having an excellent camera it is also very powerful, has decent battery life, a 1920 x 1080 (401ppi) 5.5 inch display and is under £400, it competes with top phones at a brilliant price