On Monday, just hours before Boris Johnson pushed back Freedom Day by four weeks, the Government published new modelling, warning that a deadly third wave was on the horizon.

Under the most pessimistic scenario, Imperial College estimated Britain could experience a further 203,824 deaths by next June, while even modest estimates from rival groups suggested more than 50,000 would die.

Yet it has now emerged the models were based on out-of-date estimates of vaccine effectiveness, which assumed far fewer people protected by the jabs.

Imperial was working on the basis that the AstraZeneca jab would reduce hospitalisations by between 77 and 87 per cent after two doses, while the London School of Hygiene and Tropical Medicine (LSHTM) suggested 81 to 90 per cent, and the University of Warwick put it a little higher – between 86 and 95 per cent.

We now know from real-world Public Health England (PHE) data that the AstraZeneca jab is 92 per cent effective against hospitalisation. 

The effectiveness of the Pfizer jab was also underestimated by the groups, with Imperial estimating 84 to 90 per cent, LSHTM 85 to 90 per cent and Warwick 86 to 95 per cent. PHE currently estimates it is 96 per cent. 

The distinction is important because it now means that both the pessimistic and central scenarios for all groups must be wrong. For Warwick, that would mean their death estimates could fall from 72,400 to 17,100. 

Switching to an optimistic scenario would also see Imperial’s death figures fall from 203,824 to 26,854. Even that is likely to be too high as even their best-case vaccine efficacy was out by five per cent. 

How modelled data underestimated the effect of vaccines

The PHE figures were made public 30 minutes after the modelling papers dropped, so it might be tempting to think that the new data came too late to make a difference. 

Yet at Wednesday’s science and technology select committee, Dr Susan Hopkins, the deputy director of PHE’s national infection service, told MPs that the Government had known about the figures since last Friday.

It means that the Government published modelling data to bolster a delay despite already knowing it was out of date.

All the models showed a significant wave of infections in the summer, and suggested that a pause of several weeks would save thousands of lives. Yet this was based on central estimates which now cannot be correct. 

Highlighting the data discrepancy at Wednesday’s select committee, Aaron Bell, Conservative MP, said: “The models that we seem to be relying on to justify the extension of restrictions don’t appear to be using [the PHE] numbers. 

“This is really important because the number of deaths that those numbers ultimately forecast, are for people who have had both doses, so if they have been using numbers that are now superseded, doesn’t that alter the case for the continuation of restrictions?”

“We are voting in the House of Commons on the basis of those models. And it’s obviously very good news. These numbers are coming out so far ahead of even the optimistic scenarios that have been modelled.”

The debacle was neatly summed up by committee chair Greg Clark, who asked the panel of experts: “The models would look different if we plugged in the new data? Everyone’s nodding.”

Mr Clark, the former science minister, pointed out that the pandemic had been “beset by uncertainties and difficulties with modelling evidence informing government policy decisions” and queried why the real-world data hadn’t been given precedence. 

“Wouldn’t it have been possible given the relatively new real world data, to say actually, in the light of this data, we need a few more days to assess it, before we decide what is going to be the right implications of public policy?”

He called for the modellers to re-run the models based on the new data as soon as possible “so that, as the Prime Minister promised, a reappraisal can be made and a change made if it’s justified”.

Prof Hopkins said she had “no doubt” that the modellers would re-run the models based on the new data, yet it is likely to be too late to make a difference. 

Back in February, the Scientific Pandemic Influenza Group on Modelling (SPI-M) also underestimated vaccine effectiveness in models used to inform the roadmap.

At the time, scientists believed jabs would reduce the risk of infection between 24 and 48 per cent after the first dose, and 30 to 60 per cent after the second dose. 

But real world results were already showing that Pfizer was reducing the risk of infection by 70 per cent after one dose and 85 per cent after the second dose. 

Latest UK vaccine numbers: rollout figures

The models were indeed re-run with the updated figures, and eye-watering death estimates reduced. Yet the roadmap was never revised and the changes never acknowledged by the Government.

We can only hope this time will be different. Although cases and admissions are rising, the numbers are still very low. Dr Hopkins admitted only around one per cent of beds in the NHS are currently being used by Covid patients, with little chance of the health service being overwhelmed.

This is hardly surprising when you consider that in 12 of the last 13 weeks there have been fewer deaths than expected compared with the five-year average, with England and Wales currently 4.8 per cent below the five-year average for deaths. 

As University of Oxford vaccine lead Professor Sir Andrew Pollard remarked at Wednesday’s select committee hearing: “If we don’t have very high hospitalisations despite the spread, the public health crisis is over.

“As long as people continue to get vaccinated,” he added: “We’re in a very good position.”