So nobody has spotted my stupid mistake?
No apology I am afraid! Absolutely no chance.
This question was on Mastermind some many years ago! And the same misconception always comes up.
Whilst possibly pedantic; I will explain,

overtaking is NOT ILLEGAL at Doubly Whites (DW) when the unbroken line is closest or nearest to you. CROSSONG or as the HC says, STRADDLING the unbroken line is a no no (apart from exemptions).
I was out today and there were several times where I indicated that I was moving out of my normal position (Secondary to be honest) and hugged the verge - whilst not riding in the cack and crud. Making it very clear that I was ready and prepared for the overtake so as not to hold up the car/s behind. I was doing more than 10mph on all but one hill/occurrence.
Near me, there is a bitch of a hill and the road/lanes are plenty wide enough for an overtake without CROSSING the DW nearest us.
It is the unsafe etc etc CROSSING of the DW if the DW is nearest to you that is 'illegal'! Not the OVERTAKE.
Pedantry aside - the 'no overtaking' answer on Mastermind was INCORRECT - the correct answer was no CROSSING etc etc.
I am freely accepting apologies myself Vikeonabike

(Does the beer smiley work on here?) :beer: (Or is that just Pistonheads?
ps - My mistake was not looking closely at the two pictures and Bridge in OP. On the Bridge at the top, it would clearly be madness to affect the overtake where there is clearly no space. The overtake itself is not the illegal activity. SOrry if pedantic but it is one of my little bug bears
pps - WOuld a motorbike overtaking the OP or a cyclist be illegal? Clearly not if it doesn't cross the DW?