Venison is the term normally used to for the meat of the deer. Furthermore, deer meet the requirements for meat to be kosher - the animals chew the cud and have a cloven hoof. Same as cows and sheep. Therefore, in many countries, Venison is available from Kosher butchers and restaurants.
But not in London or the rest of the UK. Why?
The reason is nothing to do with Jewish laws - it's actually to do with English laws. English law prohibits taking deer back to an Abattoir (a slaughterhouse) - they have to be killed in the open field. And of course, traditionally, this was done by shooting them. However, for meat to be Kosher, not only must it come from a Kosher animal, it must be slaughtered in a specific way. And it must be in perfect health before it is slaughtered. Peppered with little lead pellets doesn't count as perfect health!
So, as things stand, there is no Kosher Venison in the UK.
Interestingly enough, back in the early 20th century, the Rothschild family (a prominent Jewish family) had a large ranch in the SouthWest of England. And there were deer on this ranch. Once a year, some Rabbis who knew how to slaughter animals in the appropriate method would travel to the ranch, and run around the fields trying to catch some deer. When they caught them, they would slaughter them immediately - therefore keeping in line with both the Jewish and English law. So once a year, there was a supply of Kosher venison to the Jewish market.
DejaMorgana says "I would have loved to see a bunch of rabbis running around trying to catch a perfectly healthy deer for shkhitah!". I'll second that!