The couple have released an open letter addressed to the PM after they were named ambassadors of charity Alzheimer’s Society.
They are now encouraging the public to sign it before it is delivered to 10 Downing Street in September.
Barbara – best known as EastEnders’ Peggy Mitchell – was diagnosed with Alzheimer’s disease in 2014 and publicly revealed the news last year.
In a statement calling for people to get behind the new campaign, she said: “I am absolutely delighted to become an ambassador for this wonderful charity, who are helping so many people living with dementia… like me.
“We’re lucky to have amazing support but my heart goes out to the many, many people who are really struggling to get the care they so desperately need.
“Please join us – let’s do everything we can to sort this out.”
Scott said he wanted to “do everything I can” to help those who face a “constant battle to get what they need” after spending the last four months meeting other people living with dementia and their families.
He said: “The last few years have been really hard for both Barbara and I as we’ve had to get used to dementia being in our lives.
“Alzheimer’s Society has shown us there is life after dementia, and we want to do our bit to make sure no-one faces dementia alone.”
He continued: “The Society’s open letter to our new Prime Minister Boris Johnson to tackle the social care crisis is strongly supported by Barbara and me.
“We encourage the fantastic UK public to give their support by signing this letter. It’s time to end the battle people with dementia and their families are facing across the country.”
The Fix Dementia Care campaign calls on the Government to provide a long-term funding solution and invest in an NHS Dementia Fund.
According to the Alzheimer’s Society, dementia is the biggest health and care challenge facing the UK, as it is predicted one million people in the UK will have dementia by 2021.
Scott previously revealed Barbara has been left in need of constant care, as she can no longer be left alone.
He told The Mirror in January: “She thanks me for looking after her. I say to her, ‘You don’t have to thank me’. Barbara can’t be left alone any more. That’s the reality of it. She has to have constant care.
“She can’t look after herself but then we still sit and have dinner and watch TV and have normal conversations.”