If you wish to show a film in public, there's quite a lot to think about - not all of it copyright-related. It's certainly not just a mater of going to the DVD rental shop, or buying the disc from Amazon or somewhere - those copies will have copyright restrictions that will thwart your purpose (or land you in trouble if you breach them). Having done some delving, I thought I might usefully make the result of my research available.
To start with, you can find out what sort of licences you might need at Licences you may need to apply for - Licence Finder - GOV.UK. It covers a wide range of activities, not only showing a film. In addition to a licence covering the copyright in the film, you will also - probably - need a premises licence under the Licensing Act 2003.
The licence to show the film itself is dealt with by crossing the palms of either the Motion Picture Licensing Company Ltd or Filmbank with silver. Which of them you need to go to, depends on the film you want to show and the market sector in which you operate. Whether you are showing a single film (whether on a commercial or non-profit basis), or need an annual licence, they can usually help. Otherwise you will have to approach the distributor of the film.