If you think you can make a cross-London (or cross-Manchester, cross-Bradford, cross-Birmingham, cross-Glasgow, etc.) connection in less than the official minimum, simply start a second itinerary search from the second station based on when you think you will get there, and see what it throws up. My usual trip to Manchester includes an unofficial cross-Bradford transfer, which I have never failed to make.
Likewise, I always look for <10 minute connections at Leeds to see what time I can potentially get home. Just a shame that Delay Repay doesn't apply when the inbound train is late.