If you are going to be doing Psychology then really all you really need is a half-decent laptop with a good keyboard. I know you mentioned £800 budget but for what you are going to be doing you can really get something more than sufficient for a lot cheaper if you don't mind going older and on the used market.
I'm currently studying computer and digital forensics and for my laptop (not my main pc), I use a Lenovo ThinkPad t430 from 2013 (although upgraded outside of spec), you can get the lower end models for around £120 used but keyboard wise you would be better off buying a Lenovo Thinkpad t420. They are easily serviceable, easy to upgrade laptops at a very cheap price.
If you insist on getting new laptops I would suggest looking at more business-oriented laptops from HP or even Lenovo's latest ThinkPad (although they do have pretty subpar keyboards) as they give a good overall package with more then sufficient build quality.
In terms of metal vs plastic, it all depends on the quality of such materials. I say this because a good quality plastic laptop will always be better compared to a shoddy metal laptop and vise versa. Metal, however, is overall more durable in most cases.
A few questions before I can make a certain suggestion though...
Do you need a touchscreen/laptop hybrid?
Do you care about upgradability?
Do you care about internal storage expansion?
Do you care about the display resolution/quality/aspect ratio(only applicable on older laptops)?
Thank you.