Sometimes a tourist in London may be interested in seeing a film which has been released in the UK, but will not be released in their own country until some point in the future. Alternatively, a business traveller may be 'stuck' in London for the weekend and may opt to spend part of their weekend catching up on the latest films. In both of these cases, the traveller would want to consult an authoritative and reliable source that listed what films are showing and their screening times.
London has an entertainment district centered around Leicester Square; it is roughly analogous to Times Square in NYC in that lots of movie theatres are clustered together within a few hundred yards of each other.
Leicester Square is the centre of London's cinema land, and one of the
signs marking the Square bears the legend "Theatreland". It is claimed
that the Square contains the cinema with the largest screen and the
cinema with the most seats (over 1,600). The square is the prime
location in London for world leading film premières and co-hosts the
London Film Festival each year.9 Similar to Grauman's Chinese
Theatre in Hollywood, the square was surrounded by floor mounted
plaques with film stars' names and cast handprints. During the
2010-2012 refurbishment, nearly all of the plaques were removed except
for a few on the Vue West End cinema doorsteps.
If a given film is in the theatrical release stage, it's likely to be at one of the theatres there. While each of the theatres operates their own site, a popular strategy is to visit the square on foot and walk around between the hours of 1300 and 2100. The blockbuster films show on multiple screens and screening times are spaced about an hour apart.
For people wanting to access the exact showing times whilst simultaneously reading the reviews, a Londoner would invariably refer you to Time Out Magazine. It's usage as a canonical reference point for London entertainment predates the internet. The film listings are not restricted to the West End, but cover the whole of Greater London. The site will accept a search on "Leicester Square" and present all of their listings in that area.
As mentioned in the comments to your question, there is also VUE cinemas which (apparently) can accept a US ZIP code and/or a UK post code. VUE has the franchises at two of the largest shopping malls in the London suburbs: Westfield Stratford City and Westfield London. They also hold the franchise at what is arguably South East England's 'showcase mall', Bluewater, which has destinational status in its own right (trains depart from St Pancras).
Finally, if you wanted to attend a 'star-studded' theatrical release, possibly attended by the film's principals, there are specialist agents who can arrange this for you.
Disclaimer: I have no relationship with any of the commercial links given in this answer. Please also read Are internal tourists tourists?