For your budget, and intended use, I’d look at getting something with rigid forks (ie no suspension) as it will be lighter and more of the budget will be spent on gearing (and possible disc brakes). Plus any fork on a sub £500 bike is likely to be pretty hopeless, just add weight, and offer poor performance.
If you intend to use it daily on the roads then I’d consider a hybrid as you’ll get higher gearing, more suited to road riding.
If you have mechanical knowledge and are happy to do DIY repairs/maintenance then the classifieds could be worth a look (certainly if you can go and inspect the bike before handing over your cash). Be careful though, suspension forks can be expensive to fix if they are faulty, and things like wheel bearings, bottom brakets, headsets, chain rings, tyres etc all add up if you buy a bad ‘un. I bought a bit of a wrecker but already had a box of spares and time to fix it up, if you’re not that way inclined I’d go new from your local bike shop.