Without mandatory face masks, continued working from home and some social distancing, those for whom the vaccines do not work as well will be placed in much greater risk, the MS Society and Blood Cancer UK said.
Boris Johnson announced on Monday the end of almost all lockdown measures will go forward on 19 July, the so-called “freedom day”, including leaving it up to individuals and businesses whether they continue wearing masks.
But those with conditions which have weakened their immune system may find Covid vaccines do not work as effectively for them as others.
Gemma Peters, chief executive of Blood Cancer UK, said “freedom day” would make these more vulnerable members of society more at risk.
“People with blood cancer are both at high risk from Covid and the vaccines are unlikely to have worked as well for them because of their compromised immune systems," she said.
"The fact is that the less people wear masks and keep their distance from others, the less safe some people with blood cancer will feel to be out in public.
“This means that for many of them, July 19 will not be freedom day in England but the day more freedoms are taken away from them.”
Her message was echoed by Philip Anderson, head of policy at the MS Society, who said evidence was emerging that those with suppressed immune systems, including many living with multiple sclerosis, were not as well protected after taking the vaccine.
“This is especially concerning given many of the same people are defined by the government as ‘clinically extremely vulnerable’ to Covid-19.
"Yet as the country prepares to take less precautions, the Prime Minister has failed to make clear how those most at risk will be supported to stay safe.”
Both charities urged the government to make plans to protect those more vulnerable to Covid after restrictions ease on 19 July.
"It is imperative the government ensures vulnerable people are not pressured to stop working from home, as well as ensuring they can get food and medical care without facing crowded shops or hospitals unnecessarily,” said Mr Anderson.
Ms Peters said she was worried so far ministers were relying entirely on “asking the general public to be considerate”.
"In the face of government inaction, we would appeal to everyone to help protect people with blood cancer safer by continuing to wear masks in public and continue to respect people’s social distance even after July 19,” she said.
"There’s no way of knowing if the person next to you in the supermarket or in the pub has a compromised immune system, so the more considerate you are, the safer immunocompromised people will feel."
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