Remember when they put a mohican on Churchill? That was back in 2000 during an anti-capitalism protest that turned into a riot. Interestingly, it was an ex-soldier who decided to take a strip of turf from Parliament Square and give old Winnie a modern hairstyle.

There was a good deal of understandable outrage, but it became quite a “thing”. It inspired an artwork by Banksy, based on the famous Karsh wartime photo of Churchill – the same one, by the way, that appears in more sombre tones on the back of the new fiver.

Some rather fancifully wondered whether the old boy, basically a punk in a frock coat, would have enjoyed the joke; then again his wife Clementine had a famous oil painting of Sir Winston by Graham Sutherland burned because they disliked it so much. Sutherland later called the burning of his artwork, presented to Churchill to mark his 80th birthday in 1954 (Churchill was still serving as prime minister at the time) an “act of vandalism”.

I wonder what Margaret Thatcher would make of the proposal to put a statue of herself in Parliament Square too. The idea has come under a great deal of attack (something she was well used to) from every authority remotely associated with this important national space in the centre of the capital. In a delicious turn of phrase Westminster Council describe the area as a "monument saturation zone, considered unsuitable for new memorials", and it is true that there are an awful lot of them jostling around.

Some of the more successful are the jolly Nelson Mandela one, perfectly balancing an earlier South African statesman, Jan Smuts, who looks like he’s ice skating. There’s a windswept David Lloyd George, and a boring rendering of Abraham Lincoln.

Figure of note: Churchill on the back of the new fiver (Getty)

Wander around some more and you’ll discover General Slim, Oliver Cromwell, General Haig and, in the shadow of Admiral Nelson’s mighty column, a dinky Charles I on a horse, also once targeted by the enemies of capitalism (I’m not sure if Charles I was for or against the early form of capitalism over which he ruled by divine right). Anyway there are lots of dead heroes and anti-heroes around. So yes, saturated sounds about right.

However, the main objection to the project seems to be that the “Thatch Statch”, as it should probably be nicknamed, would be in for a bit of vandalism. Not so long ago someone “decapitated” a different Thatcher statue, and of course some communities had street parties when they heard she’d died a few years ago.

I’ve no doubt that the Thatch Statch would attract tributes of all kinds, but I think that is a rather appropriate way for the nation to vent its divisions over what she did to/for the country. Like Sir Winston’s mohican, it is possible that someone might have some artistic inspiration that would itself represent a transformational work of art.

The statue of the woman who changed the face of Britain for a decade, and whose legacy lives on, deserves to be the target of artistic, vandalistic and intellectual interest. It would be fascinating to see what happened to it, and why.