The leader of the Reclaim Party said he had been inspired to try and topple City Hall incumbent Sadiq Khan at the May 6 election after the Chancellor revealed at the Budget that the coronavirus response had seen the Government borrow £407 billion.
Mr Fox said it amounted to "roughly £1,600 for every family in the country" and had led to Rishi Sunak to increase the tax burden to its "highest level for 50 years".
In a statement, he said it was time to get the financial situation "under control" and vowed to push for the lockdown to be eased immediately after the local elections - more than a month earlier than currently planned under the Prime Minister's road map for lifting all restrictions.
"Every week that goes by without lifting lockdown means more lost jobs, more lost businesses and even more taxes in the future," Mr Fox said.
"That's why I am standing for London mayor.
"With almost all older and vulnerable people having got their jab, I want the lockdown lifted straight away.
"The Government has said vaccines are working, hospitalisations and deaths are tumbling, but we are still being told we won't be able to resume normal life until mid-summer at the earliest.
"Both the main parties are competing in this dreary race to be the last to set the country free.
"Both Tory and Labour have got this badly wrong. I want London - and indeed the rest of the country - to be allowed to get back to work and play immediately - not by late June."
The party said a survey carried out on its behalf by Savanta ComRes found that more than half of all Londoners want the national lockdown lifted by the end of May, with young people in the capital even keener on a swift exit from lockdown than the older generation.
They said the poll saw 1,002 London adults, aged 18 or older, interviewed online from February 18-22.
Mr Fox has become an outspoken critic against both Covid-19 lockdowns and so-called "wokeism".
The television and film actor faced a backlash online in November for a tweet in which he claimed to have had people over for dinner and appeared to criticise the NHS.
"Just had a large group over to lunch and we hugged and ate and talked and put the world to rights," he said.
"If the NHS can't cope, then the NHS isn't fit for purpose."
The announcement comes only days after Mr Khan kicked off his own campaign to be re-elected as the Mayor of London by calling for a post-war style economic recovery package for the capital.
The former Labour minister said that "jobs, jobs, jobs" for Londoners affected by the coronavirus crisis will be a top priority if he wins a fresh mandate in the May election.
Reporting by PA