Cyclists can be vulnerable to other traffic. That vulnerability can be eased quite substantially by drivers modifying their driving habits slightly. This is not always obvious when drivers are embroiled in 'making progress' or getting to their destination quickly, but a simple rule to follow is to: treat a cyclist like any other vehicle. It may slow other traffic down a little or delay drivers by a few seconds but the cyclist will appreciate the respect given for their safety and it will help make the roads safer and more pleasant for everyone.
Whether you are approaching from behind or going for the overtake, slow down and keep a safe distance both from behind and when passing. It is very unnerving for a cyclist to have someone driving a few feet behind them or passing them within a few feet to the side especially at speed. The unnerving worsens with increased speed and/or a decrease in the space given.
Sometimes drivers need to wait a few moments until there is enough width in the road and there is no oncoming traffic to enable them to pass safely. Drivers also need to look ahead to make sure there is enough space to complete the manoeuvre before the road narrows or there could be oncoming traffic to come into conflict with such as on a bend or brow of a hill. If the driving speed is above about 30 mph, driversreally should give a complete cars width when overtaking,so wait until there is no oncoming traffic and use the oncoming lane. Or with multiple lanes, use the next lane like you would when overtaking a car.
Many drivers have a tendency to 'follow through' when the vehicle in front overtakes a cyclist. With each car following through, each car tends to come closer to the cyclist until there is little or no more space left for safety. This is often caused by reaching a narrowing of the road or if there is oncoming traffic. Keeping a greater distance from the vehicle in front helps drivers to spot cyclists earlier and make a better and more informed overtaking choice along with a safer manoeuvre. You wouldn't just follow though when overtaking another car so try not to be tempted to do this when overtaking cyclists.