Video report by David Hirst
Public health experts across the region say now is not the time for anyone to let down their guard.
There is concern in Wakefield - which has the worst Covid rates in West Yorkshire - as infection levels are well above the national average.
Wakefield council is asking residents to remain cautious and careful as they return to the region's high streets.
Local businesses say they are thrilled to be back and looking forward to returning to normality.
The authority has launched a 'welcome back' video to emphasise the importance of hygiene and making space for others.
In Hull it is a similar picture with cases three times higher than elsewhere in the country.
Customers have enjoyed a cautious welcome back to the high street in the city as Covid restrictions continue to ease.
Shops are experiencing brisk trade and many pub gardens are fully booked as non-essential shops open and outdoor hospitality is allowed.
Police and health chiefs are warning people not to take their new-found freedoms for granted and to continue to follow the rules. Sally Simpson reports.
Assistant Chief Constable Darren Downs, of Humberside Police, said: "We are pleased that the majority of the region enjoyed their first evening of socialising in local establishments.
"We did see some incidents reported but they had no direct connection to the lockdown restrictions easing and involved disputes between families and friends.
"I would take this opportunity to remind people that we still remain in a situation where we need be responsible for our actions, and make sure we observe social distancing guidance that is in place for the safety and wellbeing of everyone.
"People should remain vigilant and do everything they can to continue to prevent the spread of the virus. Whilst restrictions have eased, adhering to guidelines to prevent the virus spreading must remain a top priority."
The prime minister said people "have got to understand" the risks of reopening pubs, shops and hairdressers but he'd seen no reason to redraw the roadmap.
A government expert earlier warned if a third wave took hold, up to 50,000 people could die.
The government has now begun phase two of the vaccination programme, which targets adults aged 40-49.
The next group after over-40s will be adults aged 30-39, and then all adults aged 18-29.
The government has pledged that all UK adults will be offered their first dose by the end of July.