A re-vamp of motoring offences is badly needed. I see no problem in principle with covering pedal cycles (and horseists and whatever) under the same laws, so speed limits would apply to bicycles and cyclists could be charged with drink driving or dangerous driving. Then everyone knows where they stand, and cyclists can carry on as normal.
The lighting regulations for cycles need to be dragged kicking and screaming into the century of the fruitbat. I'd be in favour of something like the German or Dutch regs - let's mandate static dynamo/e-bike battery powered lighting with sensible beams at point of sale, unless the bike is designed for racing or off-road riding. Make pedal reflectors optional, while we're at it.
On the face of it It makes sense but:
Issue of rider knowing their speed.
Issue of what proper stopping distance is at that speed on a horse/bike (not the same as a car so speed limit should be different)
Travelling at different speeds would mean that drinking limits could be different (also the horse can bring you home when you're too drunk to navigate).
Mandatory lights/dynamos mean that either all bikes get much more expensive (a serious issue for anyone, especially with kids) or the Dynamo/lights are not that great, which is as much of an issue as not having them (my experience of bikes in Germany was very poor Dynamo lighting).
Which is why it needs quite a bit of considered thought.
It also seems to me that possibly what we need is local, not national laws. In London we have a large mass of new cyclists riding dangerously; but in the Midlands we still have very few cyclists. Why regulate nationally for a local problem (even if it is in London)?