The UK’s daily coronavirus death toll will rise from 34 to 100 a day in three to four weeks’ time, an expert on the government’s Scientific Advisory Group for Emergencies (Sage) has warned.

Infectious disease modelling expert Prof Graham Medley said there is little that can be done now to prevent daily deaths climbing to 100 – but that “we need to make sure transmission comes down now” to prevent the figure increasing further.

Medley told BBC Radio 4’s Today programme: “The treatments [for Covid-19] have improved, the way the virus is transmitting is going to be different, but nonetheless it is a dangerous virus and inevitably it will lead to some deaths.”

He said that even if only 0.8% of infections lead to deaths, down from an estimated 1% in February and March, “it still means that we are going to see deaths increase”.

He projected the UK would see 100 deaths a day in three to four weeks based on the number of cases the country is seeing now (there were 6,874 new cases on Friday) a figure he said is doubling every 10 days.

“In order to stop that process increasing again, then we need to make sure that that transmission comes down now, because that doubling time will carry on. The things that we do now will not stop 100 people dying a day, but they will stop that progressing much higher.”

On Friday, new coronavirus restrictions were announced for Leeds, parts of Wales and more towns in the north-west, bringing the numbers affected by stricter measures across the UK to 21.3 million.

The Welsh government has announced that Cardiff, Swansea and some parts of Llanelli in south Wales will be subject to local lockdowns from this weekend. Meanwhile restrictions on household mixing were announced for Blackpool, Wigan, Stockport and Leeds.

The Welsh health minister, Vaughan Gething, said the situation was “real and very serious”, with coronavirus transmission driven by households mixing indoors and in pubs.

Speaking on BBC Breakfast on Saturday, he said: “I’d say we are in a comparable place to the end of February and, of course, we ended large parts of NHS activity about two weeks later, we were in full lockdown three and a bit weeks later.”

Councillor Judith Blake, leader of Leeds city council, said that new lockdown restrictions may not be enough to halt the spread of the virus on their own.

“We know that the restrictions themselves won’t just work on their own, it has to come as part of a whole raft of measures,” she told BBC Radio 4’s Today programme.

“The important message that we know from other areas is there is a lot of confusion, a lack of clarity, particularly in areas where there are different rules in one borough and the next-door borough has another one. This has to be a wake-up call to people.”

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