MPs Olivia Blake, Louise Haigh and Gill Furniss as well as local councillors backed the campaign which calls for a change in the rules.
It comes as the Health Secretary Matt Hancock announced a pilot giving key visitors access to tests in some care homes in the south in the hope of getting testing in every care home by Christmas.
The politicians received emails and letters urging them to put pressure on the Government, and a national campaign, Rights for Residents, gathered nearly 200,000 signatures on its petition.
Ms Haigh, MP for Sheffield Heeley, said: “Coronavirus has taken an enormous toll on care home residents and their families. Many residents have been separated from their loved ones for months and it’s been utterly heartbreaking to hear from local families who have been prevented from visiting partners, parents and siblings.
“For care home residents, contact with loved ones is not just ‘nice to have’, it’s crucial for their physical and mental wellbeing. Family members should be treated as key workers – with access to weekly testing and proper PPE – so they can safely start visiting again.”
This week the Government started a pilot to enable meaningful contact across 20 care homes in Hampshire, Devon and Cornwall.
But it will be some weeks before Sheffield could see this, as a phased rollout across the country depends on the pilot’s success and transmission rates.
Current methods for visiting suggested by the government were criticised for not enabling meaningful contact, potentially distressing those with dementia and possibly backfiring in care homes that do not have the resources and therefore may shut down visits altogether.
Ms Furniss, MP for Brightside and Hillsborough said: “It is welcome that care home visits are permitted under the new lockdown measures, however I am concerned by the potential barriers to this which have been raised by constituents and organisations such as the Alzheimer’s Society.
“It is vital care homes are given the resources they need to allow families to visit in a safe, Covid-secure way. I support calls to give designated family members key worker status to allow them to access regular testing so we can bring families back together again.”
Ms Blake, MP for Sheffield Hallam, wrote to Mr Hancock last week urging him to meet the demands.
She wrote: “For those suffering from dementia, social isolation has consequences for their condition. Without exercising their cognitive skills, it makes it far more likely they will lose them.”
Local councillors also joined calls.
Sheffield Green Party leader Douglas Johnson said: “If you are living in a care home it is absolutely vital to have as much contact as possible with family and friends. It’s heartbreaking for relatives where they can’t give their mum or dad or sister a hug when they need it.”
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