What did you think when you entered "pub theatre London" in your favourite search engine and this website came up?
http://www.visitlondon.com/events/theatre/pub-theatres-in-london

The list of pub theatres at the Visit London site is so limited and so weird there's clearly some undeclared bias in the site - like it only lists whoever's paid, or whoever's a member of some club. Whatever: it's not to be trusted.

Self-evidently, recommendations three months out for fringe theatres are pointless. Many don't even know what they'll be putting on in a month's time, never mind whether it'll be any good. Even the very best, almost by definition, put on as many clunkers as works of genius.

For a full list of all London theatrical venues (pubs are a pretty minor part of London's fringe theatrical scene): the menu bar at the left of http://www.londontheatre.co.uk/index.html The pub list this takes you to is objectively compiled and complete.

For a bit more selectiveness about non-West End places (most Londoners do most of their theatre going in off-west end subsidised, or at least not for profit, theatres such as the National, the Barbican, the Royal Court, the Almeida and the Old Vic), the links under "What's on at" towards the bottom of http://www.timeout.com/london/theatre/.

Because of the ephemerality of much of the non West End scene, it's probably unrealistic for foreign visitors to preplan what they're going to see. It's probably best to buy a hard copy of the current Time Out at their departure airport or station (a number of newsagents at JFK, Schiphol, CDG and the Gare du Nord sell the current edition) or if you're arriving by plane buy it at the newsagent in the Arrivals area. Use your journey into town to plan and book from your hotel. In my experience, the whole point of the real fringe is not knowing whether that Hamlet in Serbo-Croat in a temporarily unoccupied launderette is going to work or not.

Otherwise, the theatres under the "What's on at" line on the Time Out theatre page are the group most likely to be showing non-formulaic, interesting original productions with longish planning horizons and easily accessible web booking engines.

Some theatres that put on some great 'off-West End' theatre:

The National
The Old Vic
The Menier Chocolate Factory
The Almeida
Donmar Warehouse

You might find this website of interest:
http://www.offwestend.com/

I don't think there's any problem booking now for some shows in September. For some of the better ones, I'd heartily recommend it.