Police have been responding to reports of illegal gatherings after rules were brought in just before the bank holiday weekend.
The new rules came into force on Friday, prompted by more than 1,000 unlicensed events since the end of June.
Anyone in breach of the rules could be fined £10,000.
People not wearing masks and those attending the unlawful gatherings can be fined at least £100, doubling for repeat offenders to a maximum of £3,200.
Essex Police said they had seized thousands of pounds of equipment before an unlicensed music event due to have taken place in Harlow on Saturday afternoon.
Chief Inspector Lewis Basford said: “My final message is to the organisers: we will seize the equipment – I don’t care if you’ve hired it from someone or if it’s yours, we will break up your event, and we can now fine you up to £10,000.”
West Midlands Police said early on Sunday it had dealt with about 90 reports from the public about possible breaches of restrictions “but we’ve not had to use our enforcement powers”.
“Tonight has been dominated by reports of house parties, rather than the really big gatherings we’ve seen earlier in recent weeks.”
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In West Yorkshire, a man was arrested after acting as the DJ at a street party in Harehills.
Five other people at the gathering were fined.
Superintendent Chris Bowen said: “We hope people will recognise the ongoing risks of holding or taking part in events such as this but where intervention is needed, we will fine people and make arrests.”
Home Secretary Priti Patel said the rules are in response to “the most serious breaches of social distancing restrictions”.
But Metropolitan Police Federation chairman Ken Marsh warned the legislation was unenforceable and would mean “absolutely nothing” for enforcement in London.
He told PA news: “It could be good for areas outside London, but it means absolutely nothing to us here.
“People just set up a music box in the middle of the street and say ‘it’s not mine’, it’s utter nonsense.”
He wanted laws which would let officers “be more forceful” in clearing areas.
Another police chief said the confusing guidelines were being used by some as an excuse to break the rules.
Andy Rhodes, Chief Constable of Lancashire Constabulary, said there was a “world of difference” between people acting sensibly and others who were “flagrantly” ignoring the rules.