Just down the road from the Woolwich Infant - and I think on the same bus route - is the Antigallican.
This was a name so unusual that I had to look it up, as well.
It seems that xenophobia is nothing new. The Anti-Gallican Society was formed around 1745 (according to the British Museum website, which holds a badge of one of the Presidents of the Society), to oppose French imports and French cultural influence in society. They also gave prizes for local products - a sort of early "I'm Backing Britain" campaign. The badge in the British Museum shows St George spearing the French flag.
A blog called Caroline's Miscellany mentions the pub, back in 2009.