After doing some research, it looks as though the Cineworld Unlimited card for about £12 a month is the best option to use in conjunction with Meerkat Movies, however it's the other side of the Tyne Tunnel which eats into most of the saving.
I can get discounted tickets for Odeon, Vue and Cineworld via work's online gateway (think a lot of large corporate employers have similar). When you buy one of these, you get a code you can redeem instantly online on the cinema's web page.
I think I've tried to stack this ticket with Meerkat Movies for Vue before and been knocked back (it only gave the code-purchase ticket on its own - trying to add the meerkat code knocked the code off and just showed full price plus the freemeerkat ticket.
Does anyone know if it's the same situation for Odeon and Cineworld?