Assuming that the screen is merely incidental in the overall scene there should be no copyright issues, irrespective of whether there are recognisable faces in the image. However if the television screen was the primary focus of the image there might be issues.
Bob's spot on. If the image caught is the sole focus it's akin to trying to steal the image, worse if it's for profit. If it's in the background, for example, using magazine covers as wallpaper, and one cover isn't the focus, and the sole intent isnt to infringe someones IP, you're fine. And if someone tries to invoice or sue you on this, point them to the CDPA and the inform them to kindly go away.
Just to add to what Bob and Andy G have correctly stated on this, the relevant part of the Copyright Designs and Patents Act 1988 concerning incidental inclusion is section 31. Although not relevant to this particular question because the photographs are intended for commercial use, there is another exception found in section 71 CDPA which allows the deliberate photographing of an image from a broadcast for private use purposes:
"71 Photographs of broadcasts
(1) The making in domestic premises for private and domestic use of a photograph of the whole or any part of an image forming part of a broadcast, or a copy of such a photograph, does not infringe any copyright in the broadcast or in any film included in it.
(2) Where a copy which would otherwise be an infringing copy is made in accordance with this section but is subsequently dealt with—
(a) it shall be treated as an infringing copy for the purposes of that dealing; and
(b) if that dealing infringes copyright, it shall be treated as an infringing copy for all subsequent purposes.
(3) In subsection (2), “dealt with” means sold or let for hire, offered or exposed for sale or hire or communicated to the public"
The second thing to note is that an image of a game or sport alone on a TV screen is not subject to copyright, because sports do not fall into the various categories of protected works (see the various court cases between the FAPL and Murphy). However these days, the Premier League and other organisations which license broadcast rights make sure they have their logo on screen as far as possible, since these items are subject to copyright and thus any deliberate copying of the screen would copy the logo, triggering liability for infringement.