First time poster but Axe regular, if such a confession is allowed.
In the Axe, I guess like anywhere, you need to ply a little charm and bide your time to find a girl who seems to like you as much as you like them. They all swing by robotically selling private dances, although it's a pleasure to watch them come and go at close range. If you want to be hands-on, suck tits and get your tongue on some pussy lips you want to make sure the girls are taking you up in to the £40 loft room (it's full of sofas, plenty of girls/punters, not some weird torture dungeon) not £20 downstairs, where they are more careful about security/bar staff giving them the evil eye.
Talk to them about whether they offer a 'dirty dance' and ask what goes on upstairs to make sure you're not picking one of the ones who wants the cash for as little effort as possible. Generally, things get a little more free and easy around midnight.
Although remember that the Axe is not a strip club every Saturday. It's a Rockabilly themed night some Saturdays, which is pretty good too, but obviously don't drink too much and confuse the two - you'll up in a world of trouble asking ladies when they plan to get their tits out on stage.
The pound glass at the Axe can also go into hyper mode - doing the rounds every 3 or 4 minutes, which adds up fast.
The Rainbow down the road (adding to what others have already said) can be quite good fun. Touching and getting intimate for the higher dance prices is common, but I've always felt the dances were shorter and a bit routine. The Rainbow is smaller and tends to be packed. The girls are as nice to look at as the Axe but a bit moodier. Although the pound glass seems to be pretty slow in circulating.
I used to pop in to the Steam & Sun near Euston too, although not a strip bar. But I don't think that is still there.