Hi there, London has two main arcades for 3rd strike. The Trocadero (troc) and Casino. I guess you will be using public transport so for both those arcades its best to use the London Underground tube(or to you, the subway :)). For Troc you wanna get to piccadilly circus station its on the piccadilly line and the bakerloo line, one of the exits will lead you directly into the basement floor of troc (just ask staff at the station for the exit). then take the escalators to get to the ground floor and then take the escalators to get to the first floor, then once you come off the escalator turn right you will see loads of amusment and games machines of all types, and head all the way to the end so you walk underneath the escalator that goes to the next floor (there are some fighting games under the escalator). Then look to your left and you will see a small set of steps, and thats where the versus city machines are with 3rd strike, japanese sticks and buttons.
For Casino you can again use the London underground tube to get to goodge street station on the northern line. come out of the station and turn right, walk past kfc, cex and then casino is there, the games are all in the basement and 3rd strike is on a 50 inch sit down megalo cabinet with japanese sticks and buttons.
Regarding when to go, troc practically any evening and you will hopefully find at least 2-3 challengers, maybe less unfortunately. But still some of the challengers are very strong. For casino you should go on a friday evening as thats when there are usually a lot of challengers for 3s. Both the arcades are actually within walking distance of each other (10 mins) so particularly on a friday if one place is dead its always worth checking out the other. As well as neoempire, join up to www.rankingbattles.co.uk. A lot of players and arcade regulars also post there. Both websites now and again have information on tournaments, ranking battles etc.
If I know when your gonna be down and if I can make it then I would love to give you a few games and money match (small stakes of course).