Writing reviews of games should not be a problem. You can even include screenshots and possibly the cover of the game using the exception contained in section 30
of the Copyright Designs and Patents Act 1988. The key thing to remember is to use only the bare minimum necessary to make your point - that would constitute 'fair dealing' and also meet US fair use crriteria (see section 107
of the US Copyright Act), and you must credit the game's maker.
Quoting small snippets from other people's reviews would also be OK
on the same basis, as long as you use no more than is absolutely essential and you credit the author of the other review. However if you wanted to create links to other reviews, that would be much safer as long as your links don't bypass any paywalls or similar restrictions on site access.
You are right that US fair use law differs from what is acceptable in the UK, but if you are based in the UK you need to think in terms of complying with UK law.
And there is nothing to stop you creating revenue from your reviews. Both of the exceptions I noted above can be used for commercial purposes. Just as a precaution, make sure you acknowledge the gamesmakers' trade marks. This is in case users of your site might be confused into thinking you were somehow connected to the makers, and were promoting their games.