Lord Lawson has been accused of hypocrisy by anti-Brexit campaigners after it emerged he is applying for a French residency card.
The Conservative peer, who chaired the Vote Leave campaign, said he had started the "tiresome" paperwork to prove he is legally resident in France.
But he stressed he was not applying for French citizenship, in an interview with a French magazine.
Conservative MP Sarah Wollaston said it created an "awful" impression.
Ms Wollaston, who initially campaigned to leave the EU before switching sides to vote Remain, tweeted:
End of Twitter post by @sarahwollaston
Anti-Brexit campaign Best for Britain. said the thought of Lord Lawson applying for a French residency card "takes the biscuit".
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"It seemed to Lawson that no cost was not worth paying to leave," its spokesman Paul Butters said.
"But with this news, it seems the cost will be paid by others while the former chancellor suns himself in his luxury home in France.
"The former chancellor looks like a hypocrite."
Lord Lawson, who lives in a country house in Gers, south-west France, told BBC News: "It is well known that I live in France and have done so for many years and have referred to this in the House of Lords and elsewhere.
"It was the French authorities who told me that I should apply for a carte de sejour. Nothing else has changed."
A carte de sejour shows a person is legally resident in France and it is hoped possession of such documentation will help avoid complications after Brexit.
In his interview with Connexion, an English-language French magazine for expats, Lord Lawson said he believes the issue of Britons living in other EU countries will be sorted out in Brexit talks but that trade was a "problem", along with the Irish border issue.
"I think the issue could be no trade deal. There will be agreement on expats and security," he said.
"It's not helped by the fact the current government is weak and is not doing a particularly good job. But that's a fact of life.
"I think the most likely outcome is initially no trade deal, then after Britain is fully out of the EU and passions have cooled there will be agreement at a future date."
Asked if he had applied for a carte de sejour, Lord Lawson said: "Yes I've just started, and don't know how it will work out, but am not particularly worried.
"It comes under the category of 'tiresome' rather than 'serious'. I understand some people are worried about healthcare cover and hope it will be sorted out.
"Speaking as a Brit in France - and I'm not applying for French nationality - I am not worried."
Lord Lawson said said Brexit would provide benefits to Britain but it depended on the policies of the government of the day.
"There are things we'd like to do that we can't now because we don't have the autonomy. But that control can be used competently or not.
"If it is, I believe the UK will benefit increasingly over the years, if not, we'll suffer."