Story I've heard, second-hand but from someone who was apparently 'there', I'll leave it up to yourselves to decide whether it's true, or how much truth is in it.
(I told this story to my brother, he's an ex-bike cop and he says that when you're on a bike you're a biker first and a bobby second.)
Anyway - this lad and three or four of his mates were on their motorbikes, fairly high-powered stuff, on a weekend jaunt. They always behave very sensibly in town and when there's traffic around but would let rip in the country.
They were doing 30 in a 30 limit and noticed that a couple of police motorcyclists were behind them / following them. They weren't doing anything wrong so weren't concerned. The police followed them for about 15 minutes through a variety of road conditions and obviously decided these lads were good motorcyclists.
They then hit a national speed limit area and naturally the lads increased their speed up to 60, but no more as there were police behind them.
One of the police motorcyclists then overtook them, and started slowing down. The lads were a bit confused by this, but as there were no signals from the police they would overtake when they could, but stick to 60.
This overtaking / slowing down happened 3 or 4 times in the countryside, one of the lads got p!ssed off and just thought foook this, and really let rip, overtaking the police motorcyclist in front.
Anyway - the police started racing the lads, hitting 100-120 mph on country roads. This went on for miles and miles.
They hit a town and the police peeled off, giving the lads 'thumbs ups' but reminding them also to 'calm down' with hand signals (think Harry Enfield's Scousers

)
Just shows you - the police are human too - and so long as you are seen to be behaving yourself you'll be left well alone.
M