The new law limits all social gatherings indoors and outdoors to six people only, whatever their age.
Those who break the rules can be fined from £100 to £3,200.
Chief Inspector Pat Coates,silver commander for Lincolnshire Police’s Coronavirus response said the police would only be enforcing the new law as a last resort, but said : “This is the law and this is what you must do.,
“It is everybody’s responsibility to comply with that guidance.”
He went on: “The Coronavirus is still a pandemic that is circulation in our society and we need to take measures to make sure that everybody is safe and stop that transmission.
“We will follow the four Es. Engage, explain, encourage and we will only enforce as a last resort.
“That’s the approach we’ve taken throughout the regulations and throughout lockdown.
“Please take personal responsibility and follow the new law and the new guidance.”
There are some exceptions to the rule of six, including households or support bubbles larger than six, work and education, weddings and funerals, and team sports.
The Government brought in the change after a rapid increase in the number of daily positive cases.
The rule applies across England and replaces the existing ban on participating in gatherings of more than 30 and the current guidance on allowing two households to meet indoors.
Organisers and facilitators of larger gatherings of more than 30 people – such as unlicensed music events – can still be subject to fines of up to £10,000.