Richmond Park = Full of tossers

I got pulled over for doing that, apparently it's "okay" for motorists to overtake cyclists on solid line, but not the other way round...

Yep, that's pretty much how the law is worded:-

HWC Rule 129

Double white lines where the line nearest you is solid. This means you MUST NOT cross or straddle it unless it is safe and you need to enter adjoining premises or a side road. You may cross the line if necessary, provided the road is clear, to pass a stationary vehicle, or overtake a pedal cycle, horse or road maintenance vehicle, if they are travelling at 10 mph (16 km/h) or less.
Laws RTA 1988 sect 36 & TSRGD regs 10 & 26

RSRGD reg 26 contains the gory details here:- http://www.legislation.gov.uk/uksi/2002/3113/regulation/26/made

So, as a cyclist, you can cross the solid white lines to overtake a stationary vehicle, a pedal cycle moving at 10mph or less, a horse moving at 10mph or less, but not a car moving at 10mph or less.

Can't recall the white line situation - it was coming down Sawyer's Hill.