I've brought both the Star Wars LCG & Android: Netrunner in to London on Board. Only on Sundays though and always with enough decks for people who don't own the game to be able to play as well.
The reason for there not being much LCG playing at LoB is that a) they're mostly two player which means two people are taking a table that 4+ could be playing at and b) the pre-constructed decks aspect can result in the games not being very open to people who haven't bought in already.
The first one is less of an issue on Sunday as it's an all day event and a lot people will have left by sevenish leaving plenty of room for two player board & card games for people who are good with staying late (I imagine the same holds true for the Saturday events as well but can't say for sure as I only do Sunday). Since Call of the Cthulhu has multiplayer rules as well if you were to put together several beginner friendly decks you could bring it in as a group game + tutorial mode for the early part of the day and then later as tables free up play two player as well. I know if I saw you posting in the comments for a Sunday session that you were bringing it in I'd sign up for a round or two. I've never played before but the mechanics look very interesting.