From the above links...
Princess Margaret's decision not to marry Group Captain Peter Townsend, a divorcee, has always been thought to have been made under pressure and opposition from the Queen, the court and senior members within the Church of England.
But now a newly discovered letter from the Princess turns the story on its head, revealing that she was "uncertain" of her love for Townsend, despite their long-term affair. Far from being forced to act, the Princess's letter to Anthony Eden, the then prime minister, shows that she was determined to take the decision herself of whether to marry Townsend or not.
The letter also makes clear that Princess Margaret was aware that the government was paving the way for a marriage if she and Townsend wanted it. In addition, and no less important, the latest papers confirm that had the couple married, the Princess would have been required to surrender nothing more than her right of succession to the throne. She would have retained her style and rank of Royal Highness together with her Civil List annuity. That may at last put to rest the often-voiced but mistaken opinion that she chose to put the privileges of being a royal princess before everything else.
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There was no legal impediment stopping Princess Margaret from marrying Peter Townsend and under the terms of the Act of Settlement she would not have lost her place in the Line of Succession. Therefore it's curious that the government would insist on her displacement which could only be achieved by an Act of Parliament depriving her of her rights.
Given that at the time the Queen had two direct successors in Charles and Anne (making Margaret third in line) the proposition seems somewhat extreme and heavy-handed.