I work in Twickenham, Mac's right, the main pubs in Twickenham are a left turn out the station and a couple of minutes walk in the opposite direction of the stadium so not worth it if you're running late, there are no pubs on the way to the stadium from the station so best to drink in there.
Head in to Twickenham for a drink afterwards as the station will be a nightmare, if you're a real ale person then I recommend the Eel pie on Church street, walk past the station over the bridge and walk along the high street passing a Wetherspoons, pass a HSBC and cross the road, at the next corner is a Barclays, that's Church Street, the Eel Pie is near the bottom on the left. 10 minute walk from the station.