If you only ride in daylight and your bike is properly maintained, then the only legal requirement is a working brake on each wheel (But see requirement for the brakes to be efficient in the Highway Code.)
The complications start if you ride at night.
You must have front and rear lamps, pedal reflectors and a red rear reflector. These must meet either BSI ‘Kitemark’ standards (BS6102/3 Part 1 (Reflectors) Part 2 (Lights)), or the equivalent Euro standard.
The regulations on sales of new bikes require more reflectors to be fitted but you do not have to keep them on, or replace them if they drop off.
Reflectors for clipless pedals are either unobtainable or useless which is why so many new bikes are sold without pedals. If you have clipless pedals, reflective ankle bands show you are trying to comply with a stupid law.
Complications with lights:-
If you do have lamps fitted during the day, you must use them if visibility becomes poor.
Flashing lamps fitted to a bike are illegal. (Could be confused with a fire engine.)
Although LED rear lamps are very bright, lightweight, reliable and the batteries last ages, most types do not meet the British Standard.
The British Standard for front lamps includes running for 10 hours on a set of batteries. This means that most of the powerful rechargeable front lamps fail that part of the standard unless you have a car battery in your pannier. The most important point is to remember that you need to be seen by the driver of a car looking for a gap in a queue of cars with headlights on. The headlights of the emerging car will be pointing across the road so your reflectors will not help. You need the brightest front lamp you can get.
If you have a set of bright lamps, steady, flashing or strobing, you are unlikely to be prosecuted BUT, if you are knocked off in a collision with a motor vehicle, the driver’s insurance company will use any excuse to delay and reduce compensation – just when you or your heirs are least able to fight. Remember, the driver of the motor vehicle may be the only person there to give evidence.
A bike is a vehicle and you must comply with the law applying to vehicles. The best advice here is to get a copy of the Highway Code and read it, especially the rules for cyclists.
The Highway Code makes clear what is law and what is only advice. If you are knocked off while disregarding the advice, you are more likely to find the insurance company dragging its feet. For example, there is no legal requirement to dress in fluorescent yellow and twinkle like a little star, but if you are killed in a road ‘accident’ your clothing will be photographed ‘and used in evidence’. (This also applies to your grandma walking home from a bring-and-buy sale in a navy blue coat.)