Data the Government and NHS are putting out on the coronavirus vaccine rollout in England is “not good enough”, the Royal Statistical Society (RSS) has said.

A dearth of data on who is receiving coronavirus vaccines means the public cannot know how well the programme is progressing, according to Professor Jennifer Rogers, a member of the RSS Covid-19 task force.

Eight weeks into the rollout, some 5.9 million people in England and 6.8 million people in the UK have received their first dose.

But there is currently no official information on how many doses have gone to each priority group in England, which include care home residents and their carers.

The Government has also not provided estimates for how many people are in each of the priority groups, although Boris Johnson has said the top four groups total 12 million people in England and 15 million across the UK.

Daily NHS England vaccine figures show an overall number of doses, and weekly reports show a breakdown between recipients over 80 and below 80 and by region.

More detailed information is available from Public Health Wales, which publishes the number of people in each priority group and how many doses have reached them.

The RSS is calling for data to be published on how many doses have gone to each priority group, a breakdown by gender and age and which vaccine has been administered, how different settings are performing, and numbers ordered and delivered.

Prof Rogers said the available information is “not good enough to be able to answer all the questions that we might ask of this vaccine rollout”.

She told the PA news agency: “There’s so much information that we could gather about this vaccine data which is going to be so important to be able to answer all sorts of different questions.

“And the data that we have so far just really doesn’t allow us to answer many questions at all.

“And this is going to be one of the key things that’s going to help get us out of these national lockdowns and get us to the other side of this pandemic.

“It’s such an important part of this whole pandemic journey that we really need to be making sure that we fully understand where we’re at with the vaccines, where we may not be performing as well, where the gaps might be, so that we can really make sure that it’s done properly, and everybody who really needs to be protected is protected as soon as possible.”

Prof Rogers said without more detailed, regularly released data, the public cannot hold the Government to account on meeting its targets, or fully know who is being protected.

She also said it is “very important” for the Government to monitor uptake and refusal rates so it can identify any problems, including hesitancy in particular groups, and take steps to combat this.

It comes as Policy Exchange said vaccine data broken down by ethnicity, sex, age, and numbers accepted/refused must be provided to identify any problems and avoid potentially “socially divisive lockdown measures”.

Its paper says early regional figures show “substantial variation in vaccination rates, notably areas with the most ethnically diverse populations such as London featuring at the bottom of the list”.

The think tank also notes “reports of the circulation of false news, such as misinformation about the presence of alcohol or meat products in the vaccine”.

Vaccines minister Nadhim Zahawi told BBC Breakfast that vaccine data on ethnicity and occupation is being collected and will be published “very soon”.

Policy Exchange is warning that the Government may meet its target to vaccinate all in the top four priority groups by mid-February but fail to protect the poorest and those from ethnic minorities – “an equally important public health objective”.

Robert Ede, head of Policy Exchange’s health and social care unit, said: “There is much to celebrate about the current rollout. However, a lack of granular data on uptake among certain groups, and the numbers of those refusing the offer of a vaccine is worrying and threatens to undermine this good start.

“If uptake remains low in poorer, more ethnically diverse neighbourhoods, as well as higher risk of more death and serious illness further down the line, there will also be reasonable public health grounds to keep these areas under tighter restrictions while measures ease elsewhere.

“This would be a deeply undesirable situation that would amplify the health inequalities already found in society.”

It is also calling for the Government to publish monthly assessments of the impact of interventions to address vaccine hesitancy.

A spokeswoman for the NHS said: “As has been the case from the start of the vaccination programme, when someone is vaccinated this fact links to their NHS records, enabling population uptake to be monitored by ethnicity, and with aggregate data shared with local authority directors of public health as they lead work to ensure equitable community uptake.”

She added that ethnicity data is now being recorded through the IT system Pinnacle, as a  “belt-and-braces supplementary measure”.

Dr Hodon Abdi, co-chair of Royal College of Emergency Medicine’s  Equity, Diversity and Inclusion Committee, said: “This is urgent, and we hope that NHS England will use this data for forward planning and address any disparities there may be with access and availability to minority ethnic communities and those at a disproportionate risk.”