leaned heavily on the moral authority of the Monarchy which had not at that point been diluted by the scandals on the late 80's and 90's. If somehow you bought tougher the public mood towards the monarchy of 1997 with the socio-economic unrest of the late 70's you could have a very potent condition.
That said the UK has often been seen as being close to revolution, e.g. in the post Napoleonic period, but never managed it.
The public mood towards the monarchy in 1997 was fine, support for the monarchy has never dropped below 65% in the UK since regular polling began in 1969. The media had a clear agenda to shift focus from them onto anything else in 1997, the same way it is now doing in relation to press regulation.
Ultimately if the Queen was complicit in supporting a anti democratic coup she would effectively damn her reputation for history, assuming this happened post 1981 then she could look to her cousin's experience in Spain and then look further back to his brother-in-law in Greece. If it was before, Constantine's II's example would be constantly in her mind.
I think the Queen would have to insist that the coup ringleaders either go to the polls to secure a mandate or she would abdicate the British crown, that would be a true test and preserve her reputation for posterity.
Assuming the coup ringleaders refused, she could abdicate and would remain Queen of Canada, Australia etc and on the basis that those countries would have almost certainly condemned any anti-democratic coup in the UK, would probably welcome her as a permanently resident monarch and she would have gone to say Canada and become wildly popular and lauded, especially in the United States, who would have been horrified by what had happened to their staunchest ally.
Elizabeth's abdication in the face of an anti-democracy movement would have probably resulted in her becoming a global symbol of democracy and lead to her winning the Nobel Peace Prize.
