Bit more complicated than that - you can only overtake anything, cyclist, horse tractor, steam engine etc across double white lines if they are doing less than 10mph (126 km/hr) and the road ahead has to be clear. So cyclist with his go pro on will prove he was going faster and still do you.
In theory, the safe distance is enough for the cyclist to fall off sideways and you not hit them. 1.5m is what Sustrans, Cycle England etc. have all decided to try to use as a measure. In eyeball terms half a lane width is about right.
If it is a long double section of miles - like in parts of Oxfordshire, if it is clear they arte holding up a lot of traffic you might try to counter-argue that they are the ones riding without due care and consideration of other road users, since Highway Code suggests it tells you when you should be giving way, not giving you a right of way.