(Much of the content below is now endorsed by the 2022 Highway Code, where safer cycling is actively promoted, and drivers are required to take more care).
Ride a metre away from the kerb. Even more if drivers are passing too close. On narrow roads or where oncoming traffic makes it unsafe to be passed, take the centre of the lane. Riding in such a prominent position will deter drivers from overtaking when there is really not enough space to do so safely. You will also have space to manoeuvre if you need to dodge pot holes, sunken iron works, debris, or if a driver passes too close. This space is also useful if you get caught by wind or turbulence or if someone throws open a stationary car door. Remember: A Metre Matters.
Note: Only ever ride less than a metre from the kerb when you are actively inviting drivers to pass or if you are pulling over or avoiding something. You might also want to stay closer to the verge if the road is very wide AND the traffic flow is very fast such as on a dual carriageway.
Off-road cycle routes can offer some respite for the less confident rider and can be a safer alternative for children or leisure riders, but on-road cycle lanes rarely offer any form of real safety. They give the illusion of safety by visually creating separate lanes. Where cycle lanes exist, drivers tend to give cyclists less space when overtaking than if the lane were not there at all. Cycle lanes can also encourage cyclists to filter past traffic, even when it is not safe to do so. Remember: Cycle lanes can be dangerous to use.
Note: Where an on-road cycle lane is built to the government recommendation of 2 metres wide it can offer some safety to cyclists, but most on-road cycle lanes are half that, or even less. These ones are worthless, pointless and dangerous.
Not just where you don't have priority but be prepared to give way to others at all times. Drivers WILL pull out in front of you when emerging from the left, they WILL pull across your path from the right, and they WILL overtake and then find that they need to slam on their brakes right in front of you. They may also be sailing through a red light when yours is green. Pedestrians WILL step into the road in front of you and dogs WILL run amok. Give way to them all, and set a good example to all road users by obeying red lights. Remember: Give way and stop, if you need to.
Didn't you know, that many drivers have Two Wheeled Road User Blindness? While you might think that others can see you, they actually can't. So you need to help them as much as possible by wearing fluorescent, reflective, hi-vis clothing and use some lights. Even in the daytime a red flashing rear light will alert drivers that you actually exist and in poor visibility a white beam on the front will help too. Remember: Many drivers are blind, so be seen.
When the worst does happen, you do not want to be hurtling towards the kerbstone with an unprotected head or sliding down the tarmac with bare hands, so it might be an idea to invest in some protective clothing. I say 'might' because if you ride safely (see above) the chances of this happening are very slim anyway. There is also some evidence to suggest that cyclists wearing helmets do not overall contribute to cycle safety. Cyclists not wearing helmets my be regarded by drivers as more vulnerable and be given more space. Cyclists not wearing helmets may ride more cautiously too, so with both the drivers AND the cyclists being more cautious, this can contribute to better road safety. But the best form of protection is a Camcorder. Apart from giving useful evidence to the police or for insurance claims, when drivers know they are being recorded on video, they usually drive a lot more cautiously. Remember: Your best protection is video evidence, so wear a camera if you can.