The Nexus 4 slaughters everything else in that price range on raw power so would be a good choice if you want to play 3D games, but it's quite a bit over the 180 you want to spend and it has some serious flaws in my opinion. The cheapest version that is £239 only has 8GB, and a lot of that will be taken up by the OS, and it has no card slot so you are stuck with 8GB.
For £187 you can get the Galaxy S3 mini delivered. As the name suggests it's a smaller phone (although the screen is still as big as an iPhone 5). Whilst not as fast as the N4, it still has a perfectly decent dual core 1Ghz CPU and 1GB of RAM. Like the N4, the one for £187 only has 8GB of memory but you can add a microSD card.