The force is asking people to stick to the current lockdown which was extended for three weeks by the Government on Thursday.
Police said: “We are asking the public to continue playing their role in the ongoing battle against coronavirus by staying home and saving lives.
“Following the Government’s announcement on Thursday of a three-week extension to the current lockdown, our officers will police the county with the same approach.
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“While the vast majority of people are following guidance, some have gathered in larger groups or made non-essential journeys.
“If people aren’t sticking to the guidance then we will talk to them and encourage them to change their behaviour. If this is ignored, we will use our powers to make them leave the area or, in some cases, fine them.
“So far, we have issued 50 Fixed Penalty Notices (FPNs). This number includes two men who were fined on Wednesday having travelled from outside the county to visit Twyford Wood.”
Cambridgeshire police had issued 27 fines by Wednesday, including four in Peterborough.
Lincolnshire Police Chief Inspector Stewart Brinn said: “I appreciate the impact the lockdown has had on everyone living in the country. It has touched all of our lives, yet it does appear to be protecting the lives of friends and family.
“I would like to thank each and every one of you who are contributing to this historic national effort and following Government guidance.
“We are a police force which is rightly proud of the community we serve and we will endeavour to explain wherever possible and will enforce restrictions only as a last resort.
“The lockdown has now been in place for some weeks and there really is no excuse for not knowing what the restrictions are.
“It’s vital that we keep ourselves, and each other, safe by sticking to the guidance.”