The usual speeding laws refer to a 'motor vehicle', so they don't apply to cyclists (or pedestrians!).
As TCL has indicated, a cyclist could be charged with riding recklessly.
As far as pedestrians are concerned, there's no specific legislation but if anyone repeatedly tried to break the world record for the 100 metre sprint, on the pavements of London's busy Oxford Street, I'm sure that the police could find something in the Public Order Acts to cover the situation ;-)
Chris