I agree with all the "uh oh, Cambridge, keep the bike as cheap as possible". But at the same time, most bikes will be good as long as they are well maintained; I'm not a fan of bikes that aren't well looked after. I'm not talking about keeping the frame clean, by all means get that dirty, but the drivetrain has got to be in good condition, even if it's a really low end Shimano.
I'm also a big fan of locks, lots of GOOD quality locks. But I'm also not a fan of carrying all those locks (although if I had to, then I would, and have done multiple times). So we have to really balance this between cheap heavy bike, versus more expensive lighter bike. But TBH, £400 +/- £100 quid, most bikes will be almost similar in weight. The more expensive Trek is defo a better ride than a Carrera (I know, I have bikes of both those price ranges).
I don't think it's a good idea to claim on house insurance if the bike is stolen because that only increases the premium on the house insurance. I would leave that for more expensive claims and look into bike-specific insurance (of which I have no experience but the fine folk of cc have a wealth of knowledge, just search for it).
So, which bike do I recommend? Ugh, the heart wants a Trek FX2 but the Carrera makes more financial sense, and it is still a great bike. I have a Carrera Purva (27.5" wheels) and upgraded the tyres to Schwalbe Marathon although I reckon the standard tyres would have worked for me for a long time. IDK too much more about your situation except you're in Cambridge so I guess it's a vote for Carrera from me, plus ATLEAST TWO good quality bikes locks of DIFFERENT types (so the thief is less likely to use the same cutting tool on two different types of locks) and think about bike specific insurance.
EDIT: oh yeah, generally agree with the others about not needing a suspension fork although I have ridden suspension fork Giant and also some super-low-end "mtb" around NY and both bike were rather comfortable. Argh but it makes the bike heavier, maybe that'll get boring real quick, and like the others said.... it'll be even more of a theft magnet. Mmmh actually now I'm wondering if I actually even answered your question, OP! Sorry about that.