Why do people in UK always use handbrake?

I think its because around 95% of our cars are manual, I am currently learning to drive and have been taught to use the handbrake at red lights and maneuvers, it isn't always necessary, sometimes I forget to use my handbrake but it doesn't affect the way I drive at all, it is just a safety thing I guess, The UK are very strict on learner drivers to make sure we learn to drive the safest way possible for when we pass our tests.

You have answered your own question most people in the UK prefer manual

Most of us drive manual cars,so we are taught to use the handbrake to prevent the car "rolling" I have no idea about the brightness of rear lights,it has never come to my notice.

It's because almost all the cars are manual. You are taught to use the handbreak in this way when you learn to drive.

I use the handbrake in my manual car but not much in my automatic car. Most of our cars are manual.

Probably because we use manual cars. I drove an automatic just the once, never again!!!!

It's partly because more British cars are manual - I've never driven an automatic - and it helps to stop the car rolling where you don't want it to when you've got three pedals and both feet to think about, especially on hills. And we're taught to drive that way for safety. The British driving test is quite a stiff one: most people fail it first time. Any more than one tiny error and you fail it. Apart from having to demonstrate you can drive safely for 45 minutes, there are three required manoeuvres of which the examiner will pick two: reversing round a corner, parallel parking (reversing into a space) and 3-point turn. If you get the 3-point turn, fail to use the handbrake at the stops and you get marked down. Not only that, you don't even get to sit the test at all until you've passed the theory test, a short multiple-choice exam with a very high pass mark. So we get well trained! No bad thing in a country full of narrow roads where you really do need good control of the car.

Most cars are manual and brake lights are a lot brighter than tail lights.

You don't use them for doing a three point turn, when you learn to do a three point turn, you may, but not 'in real life' no. And no, not for a U turn either.