"(And come to think of it, I've also been known to pay an 800-quid council tax bill in 2p pieces - but that's what you get if you make me angry.)"
That would be over 280kg of coin and generally 4x the stock level held at even large of branches so you methinks your're making shit up.
Also, 2p coins can only be used to settle debt up to 20p, that is their legal tender limit. Which means any body or organisation is well within their right to reject payment made above that value.
From the Royal Mint and Bank of England:
In England and Wales the £5, £10, £20 and £50 notes are legal tender for payment of any amount. However, they are not legal tender in Scotland and Northern Ireland.
Coins are legal tender throughout the United Kingdom for the following amount:
£5 (Crown) - for any amount
£2 - for any amount
£1 - for any amount
50p - for any amount not exceeding £10
25p (Crown) - for any amount not exceeding £10
20p - for any amount not exceeding £10
10p - for any amount not exceeding £5
5p - for any amount not exceeding £5
2p - for any amount not exceeding 20p
1p - for any amount not exceeding 20p"
This also points out an other curiosity:
Yes, that is right Scottish notes are NOT legal tender outside of Scotland!
AND English money is not legal tender in Scotland.