All four FPNs were given to people in Swindon, with one issued on Tuesday and the other three issued on Thursday .
Between Monday and Sunday, Wiltshire Police issued four FPNs – bringing the overall total to 238.
They also issued 67 warnings, including four to businesses not complying, and recorded 195 Covid-related calls or online reports, which is 38 fewer than the previous week.
Officers recorded eight Covid-related crimes and 15 Covid-related incidents.
Deputy Chief Constable Paul Mills said the four FPNs issued in the past week showed that the police would take enforcement action where individuals were blatantly flouting the law.
He said: “We have been very clear that we want to focus on engagement and communication – having a visible presence in our communities, talking to people in the first instance to remind them of the law and encouraging them to follow the restrictions.
“In the case of these four FPNs, officers had already taken those steps but their warnings went unheeded and these individuals continued to deliberately flout the rules by gathering in a group and socialising.
“I would also like to acknowledge the protest in Bristol over the weekend, which our colleagues in Avon and Somerset responded to.
"The current lockdown restrictions prevent all gatherings, whether that is a small group of people drinking in the street or a large group of people protesting, and it is our duty to take action when our warnings and engagement is ignored, so that we can keep the public safe.”
Police and Crime Commissioner Angus Macpherson added: “We are now almost half way through the second national lockdown and I want to thank the vast majority of people for continuing to do their bit to stop the spread of Covid-19.
“It is clear that so many of us understand the importance of these restrictions and, despite the inconvenience or disruption this may be causing our everyday lives, I believe it will have had a really positive impact on protecting the most vulnerable in our society.”