Some records have been released from the UK archives concerning the Thatcher government and the Shah. The article in the Guardian. is an example of the coverage and the Financial Times also has coverage in their article.
The Financial Times article reports that Thatcher was "deeply unhappy" that the Shah could not be offered sanctuary in the UK in 1979. The Financial Times articles says that Thatcher confided to Lord Carrington, the foreign secretary, that the shah had been a "firm and helpful friend to the UK". As the saying goes "With friends like that who needs enemies". To call the Shah a friend of the UK shows how much the anti-Communist urge had led to tunnel vision. Thatcher along with many other politicians in the UK and the USA seemed to not really grasp the harm that was done by supporting dictatorial thugs or by continuing or supporting colonialism.
Let us not forget that it was British government who got the CIA involved in overthrowing Prime Minister Mohammad Mosaddegh in 1953 over oil. The Shah was put in place and what followed was two and a half decades of the Shah being a brutal thug. This brutality of the Shah's regime was a great contributing factor to the rise of fundamentalist forces in Iran.
The Shah was a brutal thug; not deserving of pity but rather to be taken before the bar of justice. Upon becoming Prime Minister what if Thatcher rather than being "deeply unhappy" had instead stood up and denounced the Shah as the brutal thug he was and said publicly "No entry or asylum for dictatorial brutal thugs". And what if the next day President Carter of the USA had stood up and said the same thing. If only Thatcher and Carter and a few politicians had the intelligence and courage and basic decency to be speak accurately about the Shah and demand that the Shah and his band of accomplices face justice.