Cyclists are legally obliged to follow rules of the road such as paying attention to what they are doing and where they are going, stopping at red lights, riding on the left, using one way streets in the proper direction, etc, and you can get fined for infractions.
The police can prosecute cyclists who ride dangerously, carelessly, ignore traffic signs or signals, cycle on the pavement or commit any other road traffic offence. These offences carry maximum fines between £500 and £2,500. Also, £30 fixed penalty notices can be issued for cycling on the pavement, by police and community wardens.
When used on the road during "lighting up time" which is from 30 minutes before sunset to 30 minutes after dawn, by law a bicycle must have:
* A front lamp showing a white light, positioned centrally or offside (right hand side), up to 1500mm from the ground, aligned towards and visible from the front. If capable of emitting a steady light it must be marked as conforming to BS6102/3 or an equivalent EC standard. If capable of emitting only a flashing light, it must emit at least 4 candela.
* A rear lamp showing a red light, positioned centrally or offside, between 350mm and 1500mm from the ground, at or near the rear, aligned towards and visible from behind. If capable of emitting a steady light it must be marked as conforming to BS3648, or BS6102/3, or an equivalent EC standard. If capable of emitting only a flashing light, it must emit at least 4 candela.
* A rear reflector is required, coloured red, marked BS6102/2 (or equivalent), positioned centrally or offside, between 350mm and 900mm from the ground, at or near the rear, aligned towards and visible from behind.
* Pedal reflectors four are required, coloured amber and marked BS6102/2 (or equivalent), positioned so that one is plainly visible to the front and another to the rear of each pedal.
If the bicycle does not have these, you can get street legal ones from a bicycle shop or many big stores including a chain called Halfords.
At the point of sale (ie shops) bikes have to come fitted with bells but there's no legal requirement for them to be fitted to bicycles no longer on shop display.
Section 30 Road Traffic Act 1988 says that it is an offence for a person to ride a cycle on a road or other public place when unfit to ride through drink or drugs.