Prime Minister Rishi Sunak, who like Lawson served as chancellor of the exchequer, said he had hung a picture of his illustrious predecessor when he took on the job of finance minister.
"He was a transformational Chancellor and an inspiration to me and many others," Sunak tweeted after Lawson's passing was announced late on Monday.
Former prime minister Boris Johnson mourned the loss of a political and intellectual "giant".
"He was a tax-cutter and simplifier who helped transform the economic landscape and helped millions of British people achieve their dreams," Johnson said.
After a high-profile career in journalism, focussed on business coverage, Lawson entered parliament for the Conservatives in 1974.
As chancellor in Margaret Thatcher's cabinet from 1983 to 1989, he enacted the policies of tax cutting, deregulation and privatisation that are the hallmark now of right-wing politics in Britain and beyond.
But he fell out with Thatcher towards the end of her time in office, particularly over his desire for the pound to shadow a European currency system that was a precursor of the euro.
Ironically, as a member of the House of Lords, he later came to espouse Britain's withdrawal from the European Union. He also gave intellectual heft to climate change denial.
Lawson's children include Nigella, a TV chef and writer, and prominent journalist Dominic, who like his father edited The Spectator magazine.
