There are plenty of laptops with 13.3" to 15.6" screens. The question is if there is one in the OP's budget. £400 sounds rather low so I am not sure there are any laptops with a 1080p screen in the UK with that budget.
Laptops with long battery life is not limited to thick laptops. The Dell XPS 13 is an example and so is the Lenovo ThinkPad T450s, but both costs more than £400. 17+" laptop basically has the worst battery life.