When I had a pub in that area the best pub, other than mine of course was, The Green Gate at the top of Prince Regents Lane or the Ruskin Arms in East Ham.
lads, in days gone by we always visited the railway tavern right opposite liverpool St station ( www.railwaytavern-londonec2.co.uk)... when on a visit to wes ham.
It is right on the hammersmith and city Line.... direct tubes to upton park station only nine stops away, and has good beers and big screens.
Just a thought, this would also serve to keep out of the way of the WH yoof.
Alright fella's...another Hammer here with a few tips.
Near the ground I'd only suggest The Central which is on the Barking Road. If you're coming up by train, you'll be sweet in any of the pubs near the underground stations on the way in. A lot of away fans like to drink in the Blind Beggar just to say they've been there.
As for The Railway at Liverpool St...seems an odd choice as there's plenty of pubs at Aldgate East, Whitechapel etc...and The Boleyn is much easier to get to from there. There is a Wetherspoons right next door to Aldgate East Stn thats cheap if thats any help...