Apparently, they won't ship to Canada. Sounds odd to me, but that's what I understand.
Given the amount of alcoholic beverages that get cargo'd around the world, I'm having trouble with that concept to.
Furthermore, if you look on, say, the Berry Bros. & Rudd website, they seem to have no issue in shipping to non-UK, non-EU countries.
If you're still in Central London, why not pop into a shop that facilitates FedEx shipments (e.g. one of the branches of The Color Company).
Alternatively, if you've got London based friends (or a co-operative hotel), you might look at talking to Interparcel. But as implied, they're a collection, not drop-off service.
Or if you have not bought said Gin yet, just give Berry Bros a call.... they may not be the cheapest in London, but their service is decent !