The VAULT Festival – the nearest thing to the Edinburgh Fringe you'll find in London – is well underway at Waterloo.  Each week of the Festival, we'll be picking through the programme to highlight the shows and performers we know from elsewhere.  Look out too for our reviews from VAULT, appearing throughout the Festival.

My top pick this week is Mission Abort, a taboo-busting one-woman play about making the choice to end an unwanted pregnancy. Following the protagonist's story through the discovery of her pregnancy, the decision to end it, and the return to everyday life afterwards, the script explores an experience which one in three women will go through – but which, as a society, we are surprisingly reluctant to understand. Our review of the show's Edinburgh run praised the tenderness of the performance and the quiet power of the script. Move quickly if you want to see this one, because it's on for two nights only – Wednesday and Thursday at 6:15pm.

If Mission Abort is sensitive, Droll is rough and raucous. Drolls were short comic sketches, sometimes adapted from well-known classic plays, performed by travelling players at a time in history when regular theatre was banned. Owl Schreame Theatre recreate the chaotic atmosphere of a performance in a pub, using rumbustious humour intermingled with song and dance to capture the spirit of a past age. Alongside the original Droll, there's also a new "drunken collection of winter folk plays" called The Mummers, with the two different shows performed on alternate days.

Other shows we've reviewed elsewhere include An Act Of Kindness, praised across the board in Edinburgh for its charm and warmth. My colleague Stephen Walker's review highlighted the strength of the characterisation, though he felt the story still had a little room to mature. Major Tom, meanwhile, was a hit at the VAULT last year, and returns for a limited weekend run with an incongruous combination of space exploration and the music of Bruce Springsteen.

I'm a theatre guy, so don't often dip into the comedy side of the VAULT programme, but this week sees a long list of comedians bringing one-night-only work-in-progress shows to London. Among the names we've previously reviewed well are Bridget Christie ("consistently daring and inventive"), appearing on Thursday at 9:30pm, and Josie Long ("always an interesting hybrid of the political and the whimsical"), on Friday at 6:10pm.

Also catching my eye this week: AI Love You, which intriguingly considers that if robots become human enough, they too might suffer and die. Audience voting forms a key part of the plot, and reviews from an earlier run at N16 are promising. Be Prepared slipped under my radar at Edinburgh a couple of years ago, but it too got good reviews – and its hook, that a single wrong digit in a phone number has the power to change your life, is an enticing one.

Finally, don't forget that some of the shows I picked out back at the start of the festival are still here for extended runs. Wrecked, the show in a "crashed" car, is particularly worth a look, while the Greek-myth-inspired contemporary circus Becoming Shades is well on its way to another sell-out run.