The "you are not alone" campaign aims to let anyone who may be at home with a violent or abusive partner during the lockdown know that help is still at hand through a number of agencies - the police, local authorities and national and local charities.
To show their support, a number of leaders have posted selfies having drawn a heart on their hand (see pictures attached) accompanied with the hashtag you are not alone.
Angus Macpherson, Police and Crime Commissioner, said: "Domestic Abuse is never acceptable and my office and the police are constantly publicising the message that help is out there for victims; and despite these difficult times, that same help is still available.
"Through the police, partner agencies and services we commission through the Office of Police and Crime Commissioner like Swindon's Women's Aid and Splitz, there is a wealth of support for those who are in an abusive relationship.
"There is also help for the abuser through education and rehabilitation support, again offered by our partners.
"I am keen to support initiatives like this government one because the more this sort of thing is in the public eye the more people talk about it and the more we can save people from the harm of domestic abuse."
Det Supt Ben Mant, Head of Wiltshire Police's Public Protection Department, said: "Despite the current lockdown we want to remind people that we, the police, and our partners are here if they are suffering any form of abuse.
"If you are at home with an abusive partner please reach out for help; there are a number of ways you can do this by contacting the police through 101 or 999 if it's an immediate emergency and via the number of partner agencies which can be found on our website.
"Our message is also aimed at those who abuse; despite the current situation, the police, if necessary, will arrest you and pursue a prosecution. Domestic abuse is a crime and we will investigate any reports of this kind.
"Initiatives like the government's are one of many that we are running to ensure that people know that they need not feel alone and helpless, especially at this difficult time."
Cllr David Renard, Leader of Swindon Borough Council, said: "Alongside our partners we will always be here to support victims of domestic abuse. We are happy to support this campaign to let those in need know that they can get help and we will support them to get away from an abuser safely.
"I would urge members of the public to share this campaign and all the key information we are publishing on our website and social media channels to get the message out there to victims and help us put a stop to domestic abuse in as many families and households as possible."
Wiltshire Council is also backing the government campaign and reminding residents support services are available and ready to help.
Cllr Laura Mayes, Cabinet Member for Adult Social Care, Public Health and Public Protection, said: "People need not suffer in silence. We are here to help and provide support to domestic abuse victims.
"We ask residents to be our eyes and ears and listen out for their neighbours. If they have concerns domestic abuse is happening please report it.
"We are all having to adjust in these unprecedented times but we want people to know support is still available and out there- by phone or online - people can still talk to us and we want them to have that vital support."
Cllr Pauline Church, Cabinet Member for Children, Education and Skills, said:
"Domestic abuse affects families and we know children will suffer as a result. We want parents, carers, family, friends and neighbours to be aware of how they can access help if they are a victim or are concerned for those they know and to report concerns to the Multi-Agency Safeguarding Hub where support can be accessed for them."