Reverend Sue Parfitt, 82, of Bristol and Judy Bruce, 85, a retired biology teacher from Swansea, targeted the glass enclosure around the historic document on Friday.
The pair then held up a sign reading ‘The Government is breaking the law’ before gluing themselves to the display, footage posted online on X shows.
The British Library said security had intervened to prevent further damage.
Rev Parfitt, who held a chisel while Ms Bruce used a hammer, said:
“The Magna Carta is rightly revered, being of great importance to our history, to our freedoms and to our laws.
“But there will be no freedom, no lawfulness, no rights, if we allow climate breakdown to become the catastrophe that is now threatened.”
“We must get things in proportion. The abundance of life on earth, the climate stability that allows civilisation to continue is what must be revered and protected above all else, even above our most precious artefacts.”
A statement from the British Library commented that its security team “intervened to prevent further damage to the case, which was minimal” and “the Magna Carta itself remains undamaged”.
The library said the exhibition housing the document – which sets out the principle no-one, including the king, is above the law – will be closed until further notice.
Both Ms Bruce and Reverend Parfitt were released on bail.
They are due to stand trial at Westminster Magistrates’ Court on June 20.
