Zac Goldsmith, the independent-minded Conservative MP and environmentalist, has said he will run for London mayor next year if his Richmond constituents consent to him going for the job.

His move will liven up the contest as he is entering a mostly low-profile field of Tory candidates including the entrepreneur Ivan Massow, deputy mayor Stephen Greenhalgh and London Assembly member Andrew Boff. The exception is the former England footballer Sol Campbell, who is an outsider to win the nomination.

Goldsmith, the son of the late billionaire Sir James Goldsmith and brother of Jemima Khan, would be viewed as a substantial threat to Labour, which had been hoping to walk back into City Hall after two terms served by Boris Johnson.

The main Labour contenders – Tessa Jowell, Sadiq Khan, David Lammy and Diane Abbott – will fear that Goldsmith could appeal to a broader electorate than many Tories, including Green voters, because of his history of campaigning on environmental issues and his former editorship of the Ecologist.

The move is likely to delight many Conservatives although he could be a thorn in the side of David Cameron as a well-known opponent of airport expansion at Heathrow. He is not known for toeing the party line of his leadership, having campaigned for stronger powers of recall for MPs.

Goldsmith told the Evening Standard that he had been urged to stand by people across the political spectrum and would do so if his constituents consented. He is spending tens of thousands of pounds consulting them before officially throwing his hat into the ring. “London needs a mayor who can work with government to get the resources that London needs to deal with massive pressures on housing, transport and policing but is also strong enough to stand up to the government when it gets things wrong,” he told the newspaper.

Explaining his decision to consult his constituents, he said: “I have just been re-elected as MP and it’s important to know whether or not my constituents are happy for me to run for mayor. They must have the right to say no and it is now up to them to decide without interference.”

He will now write to all 77,000 voters in Richmond Park and North Kingston, who re-elected him with a 23,015 majority, enclosing a postage-paid voting paper with the question: “Do you give your consent to Zac Goldsmith to stand for election to be mayor of London?”

In his letter to voters, he wrote: “Since being re-elected, I have been approached by many people from across the political spectrum and none, urging me to put my name forward to the Conservative candidate for mayor of London. However, I will only seek my party’s nomination for mayor with your consent.” They have until Monday 22 June to respond.

It is likely he would quit his Commons seat if elected and trigger a byelection, unlike Khan who has said he would want to serve out his term as Labour MP for Tooting. Like his friend Johnson, Goldsmith went to Eton; but Goldsmith was expelled for possessing cannabis.

Campbell declared his intention to run earlier this week, saying he thought his working-class background would help him. He told the Sun: “I’m going in with my eyes wide open. I know I’m not going to be a frontrunner. But I look at people who have been in politics for five, 10, 15 years, and muck up, you see them muck up and think ‘You guys are supposed to be pro.’

“People that have gone to Oxbridge, had thousands spent on their education, and I mean they are royally mucking up.”