It's pretty depressing to see exactly the same justifications given to riding as fast as you like as Deluded Muppets (I won't cite the actual name since it would then appear in web searches, but we all know who I'm talking about) would give for their agenda of driving as fast as you like.
Replace "pedestrian" with "cyclist" move the debate from pedestrians on cycle paths to cyclists on roads and we all sound depressingly similar.
Personally I don't mind slowing down a bit, sitting up and looking around. The park is glorious at this time of year. Even so, as the only lycra'd up rider on the path this monring, in a stream of dayglo'ed or stealthed commuters on hybrids and mountain bikes, I was amused to be the only one reminded to slow down by the copper. Despite the fact that everyone else was visibly accelerating away from me...
Personally, even if I have to slow down quite a lot, it's part of my favourite route and I'd hate to have to radically change that if I wasn't allowed to ride across the Common.