The rather daft thing, is that across the Common there are quite distinct footpaths and cyclepaths, they are a good 15-20 foot apart most of the way across. Of course, plenty of pedestrians decide that it makes more sense to walk in a cycle path that has white cycle markings, blue signs etc than to use a footpath several feet away. If I cycled on the footpath, I'd rightly be criticised, but if a pedestrian decides to wander all over the path with no regard to whether a cyclist may be coming across, then it's still my fault.
I try to avoid conflicts across that path, but you have to try and deal with people who stretch dog leads across the path, people who throw a ball for their dog
across the path as you pass, pairs of people pushing prams along it, oblivious to the rest of the world, cyclists who cycle as near to the middle of the path as they can, whilst wobbling alarmingly etc etc
I'd avoid using it, but it's too damned convenient, and the alternative would be to cycle around a very busy road, on a longer route, with some nasty right turns in it. On the plus side, I rarely go across when there are many other people around, so conflicts are always going to be minimal for me.
Suggesting that cyclists shouldn't exceed 5mph does seem somewhat ridiculous though. I'm also amazed that this is the biggest problem that they've got, since people regularly cycle on footpaths which aren't part of the cyclepath, to the extent that where the cyclepath crosses the footpath, you have to be very careful of other
cyclists more than pedestrians.