Cyclists are amongst the most vulnerable road users, and must be afforded a safe distance when overtaking. Specifically, you must give a minimum of 1.5 metres lateral distance when overtaking. In the event that the road has two or more lanes in the same direction, you must move entirely into the second lane to pass. However, on a road with a single lane, the question frequently arises as to whether you are permitted to cross a solid white line to overtake cyclists.
Solid white lines in the centre of the road must not be crossed. That means you cannot turn left into a side street, and you are not allowed to overtake. If it is a double white line and it is broken on your side, you are permitted to cross, including turning unto junctions.
However, although you are not permitted to cross a solid white line to overtake, there is an exception in the case of overtaking cyclists, and so the answer to the question is yes, you can cross a solid white line to overtake cyclists, but under a very specific condition.
The condition is quite simple, you may cross the solid white line to overtake cyclists, but only if no vehicles are approaching from the opposite direction. A vehicle can also be an approaching cyclist coming the other way, incidentally. If the road is clear, then you may proceed, allowing the cyclists the mandatory distance to pass.
If vehicles are approaching, you must not proceed. Similarly, if you cannot give the cyclist the mandatory distance, you must not proceed. Slow down, stay well back, and wait until it is safe to continue before overtaking.
Cyclists should always keep to the right to facilitate the safe passage of other road users. Although cyclists are permitted to ride two abreast, you are obliged to ride in single file to allow for the flow of traffic.
