The government has caused anger among bereaved families by telling them it will be too busy to start an inquiry into the UK’s handling of the Covid pandemic for months.

In a six-page letter to lawyers for thousands of families calling for an immediate statutory public inquiry, the government said “an inquiry now is not appropriate” and “the very people who would need to give evidence to an inquiry are working round the clock”. It said “it is not anticipated that the government’s workload will ease in the coming months”.

In a position statement that appears to kick Boris Johnson’s promise of an inquiry into the long grass, the government told the Covid-19 Bereaved Families for Justice group its “entire focus” was on delivering vaccines and preparing for “the effects of the third wave of the virus currently being experienced in neighbouring countries”. The letter, sent on 1 April, also said mechanisms to learn lessons were already in place, citing inquiries by committees of MPs and the National Audit Office (NAO).

But the bereaved families believe that with infection rates falling to the lowest levels since early September 2020 and nearly two-thirds of the adult population having received at least one vaccine dose, the launch of an inquiry is long overdue.

Jo Goodman, co-founder of the Covid bereaved group, described the government’s position as “procrastination” and “an insult to the bereaved [and] prevents the government from protecting future lives to the best of their ability”.

It sets ministers in opposition to the archbishop of Canterbury who last week told the Guardian an inquiry should start now with the power to subpoena witnesses and take evidence under oath.

He spoke as he visited the National Covid Memorial Wall in London, inscribed with more than 150,000 red hearts representing UK deaths from the virus. Labour has called for inquiry preparations to begin so it can start in earnest as soon as lockdown measures are lifted, which is currently scheduled to happen on 21 June. Other supporters of a full public inquiry include the government scientific adviser Prof John Edmunds, the head of the civil service under David Cameron, Bob Kerslake, the Royal College of Nursing and the British Medical Association.

But the government told the bereaved its “response to the pandemic is at a critical phase” and “there is simply no capacity for government to pause these efforts and divert resources to an intensive independent inquiry”.

Its position was set out in correspondence relating to a potential legal action by the bereaved against ministers. They allege the UK’s pandemic response failed to take sufficient steps to protect the public and therefore under human rights law, an inquiry must begin. The government denies this.

Ministers argue several key issues have already been investigated by parliamentary committees and the NAO which has reported on provision of ventilators, procurement of personal protective equipment, protecting the clinically vulnerable and the impact on adult social care. However, select committees cannot mandate ministers to attend and are subject to political influence, and Goodman said they amounted to “MPs marking their own homework”. She said a judge was needed.

“How long will grieving families be left without answers, without assurance that the mistakes that led to our loved one’s deaths are not repeated?” Goodman said. “We are not confident that a government can prepare effectively for future waves without first analysing and learning from the evidence as to what does and doesn’t work.”

A government spokesperson said “an independent inquiry at the appropriate time” will be part of “opportunities to look back and learn lessons”. But, they said, it is “rightly focused on protecting public health and saving lives through the vaccination programme and ongoing restrictions in place”.