There's a specific section of the Copyright Designs and Patents Act 1988 which allows small amounts of copyright material to be used for the purposes of criticism or review:
So long as the games you review have been legally made available to the public and you acknowledge the maker etc, including stills to illustrate your review will be legal.30 Criticism, review and news reporting.
(1) Fair dealing with a work for the purpose of criticism or review, of that or another work or of a performance of a work, does not infringe any copyright in the work provided that it is accompanied by a sufficient acknowledgement and provided that the work has been made available to the public.
(1A) For the purposes of subsection (1) a work has been made available to the public if it has been made available by any means, including—
(a) the issue of copies to the public;
(b) making the work available by means of an electronic retrieval system;
(c) the rental or lending of copies of the work to the public;
(d) the performance, exhibition, playing or showing of the work in public;
(e) the communication to the public of the work,
but in determining generally for the purposes of that subsection whether a work has been made available to the public no account shall be taken of any unauthorised act.
(2) Fair dealing with a work (other than a photograph) for the purpose of reporting current events does not infringe any copyright in the work provided that (subject to subsection (3)) it is accompanied by a sufficient acknowledgement.
(3) No acknowledgement is required in connection with the reporting of current events by means of a sound recording, film or broadcast where this would be impossible for reasons of practicality or otherwise.
However once your site is established, it may be beneficial for you make contact with the games manufacturers in case they feel moved to send you advance copies of new games to review.