When I lived in London, I well remember meeting the owner of a lovely collie who had to be muzzled because it had an unwelcome habit of trying to herd small children, nipping at their ankles to make them hurry up, just as it would with sheep... unsurprisingly parents in Zone 2 weren't particularly understanding.
I can never understand some people's horror about keeping dogs in London though - I had access to far more dog walking spaces within walking distance of my London flat than I ever had since moving to Wales! It's an extraordinarily dog friendly city, though I do think it helps if you get a dog that's small enough to pick up, so you can take it down a tube escalator. Few stations have lifts and the 120 steps at my local station was unappealing.
I mentioned being wary of off lead walking because of the reputation of some other dogs here locally. I would make sure I tried to go at very quiet times eg very early in the morning or take the dog to quieter parks or the countryside.
Honestly, don't do this. Go to the busiest parks at the busiest times. The logic is that the owners of dogs with interdog issues will avoid the busier times / parks and go for the quieter options, simply because it's more trouble than its worth otherwise. Your plan will bring you, disproportionately, into contact with those dogs you're trying to avoid.
Hampstead Heath was absolutely fantastic, especially around Parliament Hill; full of dogs who were all dog social because they'd either grown up walking there and were well practiced at dog interactions, or the self selecting process had weeded them out. The dogs with serious issues got either street walks or quieter spots like Highgate Wood.
To be blunt though, the sort of dogs you may be trying to avoid - the type where the younger male owners have bought them to try and look tough - almost never seem to show up in the local parks. The owners aren't the type to don wellies and a raincoat. They're either not walked, or are only taken out on errands.