I think this is such an unusual choice that it's basically going to come down to what you and your MC agree upon, like nomadzophiel said. You have taken a giant, immobile building as a piece of equipment -- one which, in my experience, is usually portrayed as small, destructible and portable, or at least movable.
In my usual reading, the 'close' tag would apply either to the proximity of the Brainer or the proximity of the target, or both. What 'close' means is highly variable, and I would say this is particularly true when you are talking about a several hundred foot tall structure. In the case of Big Ben, both readings could provide interesting limitations, but 'close' could easily be an entire neighbourhood's worth of distance.
Personally, I like the idea of 'line of sight to Big Ben' combined with the Brainer needing to actually be very close to Big Ben (like, inside it or touching it) -- this combines a more powerful than usual range of effect with an unusual territorial requirement. If it results in the Brainer just camping out at Big Ben that could be pretty lame, but since you are the player you can hopefully avoid that crutch.
That said, there are a lot of ways it could work, and see above about it coming down to a conversation between you and the MC -- and the other players.