Here are some basic tips on how to stay legal on your bike.
These are covered by the Road Vehicles Lighting Regulations which came into force in 1989 but which have been amended several times since then, making them difficult to follow. The principal requirements are that lights have to be clean, working and fitted to front (white) and rear (red).
Lights should be on when cycling between sunset and sunrise (not necessarily dark). Each day has official sunset and sunrise times. You are not breaking any laws if you fail to put on your lights when daylight visibility conditions are poor (fog) - but why would you not have your lights on? Head torches are an optional extra but do not replace a fitted front light. Flashing lights are allowed but must flash between 60 and 240 times per minute.
Reflectors are legally required only between sunset and sunrise. Cyclists need a red rear reflector and four amber pedal reflectors (one at the front and back of each pedal). Reflectors on your body do not replace these requirements. There are various exceptions - for example, bikes bought before 1975 do not need to have pedal reflectors.
The Pedal Cycles (Construction and Use) Regulations 1983 requires your bike to have two "efficient" braking systems, operating independently on the front and rear wheel, if you are using the public highway. A fixed wheel bike with a front brake is legal but not if it only has a rear brake (with no independent front wheel brake). Exceptions may apply for some tricycles, non-standard bikes and electric assist pedal cycles.