The letter, which was sent on Friday to the Shell CEO, Wael Sawan, is also supported by civil society groups including Amnesty International and Friends of the Earth.
The writer and chef Hugh Fearnley-Whittingstall, one of the signatories, said the lawsuit “beggars belief”.
“Shell boasts constantly of its green credentials, while using its vast wealth to harass climate activists who peacefully call out its climate-wrecking business practices.”
Philip Evans, a campaigner at Greenpeace UK, said: “We’re living in a world turned upside down. The UK government should be leading the way towards a future without the fossil fuels it knows are driving a cost of living crisis at home and climate chaos around the world. But instead, oil giants like Shell are handed new exploration and drilling licences that will exacerbate both crises, while they throw lawsuits against climate groups who dare to challenge them.”