Anglican priest Sue Parfitt, 82, and retired teacher Judy Bruce, 85, held a sign saying "The government is breaking the law", the group said.
Magna Carta is seen as a precursor of democracy and the basis of legal systems across the world as well as human rights conventions.
Dating from June 1215, the Great Charter -- considered one of the world's most important documents -- first put into writing the principle that the king and his government were not above the law.
London's Metropolitan police said two people had been arrested on suspicion of criminal damage and were in custody.
In a statement released by the climate action group, Parfitt said Magna Carta was "rightly revered, being of great importance to our history, to our freedoms and to our laws."
But, she added, there would be "no freedom, no lawfulness, no rights, if we allow climate breakdown to become the catastrophe that is now threatened."
The British Library holds two of four surviving copies of Magna Carta.
Just Stop Oil wants the UK government to end all new oil and gas exploration and has promised not to let up in its protests until it does so.
Its activists have targeted numerous high-profile events with stunts over the past year, including the Wimbledon tennis tournament and British Open golf tournament, as well as art galleries and museums.
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