I think the search would be great fun and shouldn't take more than a few years. One I know of is: (Those who do not wish to know the score should look away now) The Lamb Inn situated on the Hampshire / Wiltshire border, the inn is in Wiltshire but the first steps are in Hampshire. At one time the county boundary actually ran through the bar itself and as closing time was earlier in Hampshire the locals would make a rush to the Wiltshire end of the bar to obtain extra drinking time. The pub is set in an idyllic setting and you can sit in Wiltshire, look out over the village green, and during the summer watch a game of cricket taking place in Hampshire.
See http://www.inthe-newforest.co.uk/tourism/where-to-eat/starpub.htm
A google brought up at least one more.
Rod