* Prime minister ordered virtual lockdown on Monday
* Coronavirus death toll in Britain has reached 335
* People who flout new restrictions face fines (Adds poll, quotes, survey, details)
By Alistair Smout and Michael Holden
LONDON, March 24 (Reuters) - Roads were much quieter than usual on Tuesday after Britain went into virtual lockdown to try to curb the spread of the coronavirus, but London Underground trains were crammed with people and streets were far from deserted.
Some workers were also still mingling close together after Prime Minister Boris Johnson on Monday evening ordered people to stay at home, said most shops must close and banned social gatherings.
The unprecedented peacetime restrictions, which will last at least three weeks, are intended to stop the state-run National Health Service (NHS) being overwhelmed after the number of deaths from the coronavirus in Britain rose to 335.
But social media images showed London Underground railway trains were packed with commuters and one large retail chain suggested it wanted to stay open. There were also complaints that the advice was confusing or did not go far enough.
"I hope that people will follow this advice. If for any reason they don't, penalties are there," Cabinet Office minister Michael Gove told BBC TV. "People must stay at home to protect themselves, to protect the NHS and to save lives."
Under the curbs on movement, people should leave their homes only for very limited reasons such as going to supermarkets for vital supplies or for exercise once a day.
Earlier advice for Britons to avoid gatherings was widely ignored, with people flocking to parks and beauty spots. Police will now break up gatherings of more than two people, and social events such as weddings - but not funerals - will be stopped.
Gove said stronger measures than 30-pound ($35) fines for people who flouted the new restrictions could be introduced.
"If people do persist in behaving in an antisocial way, there are stronger measures that we have," he told ITV's Good Morning Britain.
A snap YouGov poll found that 93 percent of Britons supported the measures, but were split on whether fines would be a sufficient deterrent. The survey found 66 percent thought the rules would be very easy or fairly easy to follow.
Supermarkets said they had begun limiting the number of shoppers in stores at any one time and installing screens at checkouts to protect staff.
Sports Direct, a sports clothing chain owned by Frasers Group, initially indicated it would defy the order to close but later said it had asked the government for permission to open stores.
Gove said Sports Direct was not an essential shop and should close.
There was also confusion about who should be allowed to go to work and what powers police had to enforce the new guidance.
Pictures showed London Underground trains were crammed with passengers closer than the 2-metre (6-foot) recommended distance apart.
A survey showed Britain's economy was now shrinking at a record pace, faster than during the 2008-09 financial crisis as businesses across the services sector are shut.
The government has promised hundreds of billions of pounds in loan guarantees, grants and said it will pay wages. Finance minister Rishi Sunak was expected to announce new measures later on Tuesday to help the self-employed. ($1 = 0.8582 pounds) (Additional reporting by Sarah Young, Paul Sandle, James Davey and David Milliken; Writing by Michael Holden and Giles Elgood, Editing by Timothy Heritage)