Nikon D3300 vs D5300: Conclusion
Given the large number of similarities between the two cameras, it really boils down to how much you value built-in Wi-Fi, a flip-out screen and a few more AF points.
The 'guts' of both cameras are not massively different, both are made from sturdy monococque casing and both have an easy to understand graphic interface to help beginners figure out camera functions.
If money is tight we recommend going for the Nikon D3300, and if an extra £150 becomes available, put it towards an extra lens (wide-angle or macro, maybe) or a tripod.
A good lens and sturdy tripod will have more impact on the quality of your pictures than some extra AF points and built-in Wi-Fi.
As for the screen, vari-angle LCDs are nice to have, but photographers have lived without them for a long time...
Nikon D3300 vs D5300: sensor, processor, ISO
Nikon D3300 vs D5300: autofocus, continuous shooting, rear screen
Nikon D3300 vs D5300: connectivity, build quality, battery life, kit lens
Nikon D3300 vs D5300: conclusion