New coronavirus test and trace system proposed for Greater Manchester as cases rise
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It comes amid concerns people are being asked to travel miles to have tests and an appeal from Health Secretary Matt Hancock for people to only be tested if they have symptoms.
Speaking at his weekly coronavirus press conference, Mr Burnham said: "This isn't acceptable anywhere, but in Greater Manchester right now, where we need this testing capacity available to us, it's a critical issue that needs an urgent solution from the Government. We can't wait weeks for a solution."
The former Leigh MP believes a more localised approach is needed and that Greater Manchester is the right place for it.
"We have a strong integrated system here which we believe will make us the right place to do this. We urgently need a better solution than what we have got. The national test and trace system is not working in Greater Manchester," he said.
He also revealed that consideration is being given to local shielding, rather than the larger number of people shielding earlier in the pandemic, to protect the most vulnerable.
Data shared by Mr Burnham showed Greater Manchester's seven-day rate of positive tests was 59.1 in the week ending on Saturday, rising from 36.4 the week before.
He referred to Prof Kate Ardern, Wigan Council's director of public health, who he said had blamed "a huge amount of underlying virus" in the county when lockdown was lifted and people doing more socialising in the summer months.
And he noted that the current data does not yet fully take into account the impact of schools reopening in recent days.
Mr Burnham said: "Personally I believe lockdown was lifted too early in the north of England. I am talking about the original lockdown, of course, and I think that explains in part these figures."
In Wigan, the rate of positive tests rose significantly from 12.2 in the previous two weeks to 28.9.
However, it was the second lowest rate in Greater Manchester, behind Stockport at 26.2 per cent.
Asked about the rising number of coronavirus cases in Wigan, Mr Burnham said: "The infection rate is rising but it is still relatively low, and don't forget the wider context for the figures I presented today is that cases are rising all over the country, and I think Wigan is still very much closer to the national average than other Greater Manchester boroughs.
"But nevertheless of course we are concerned and we were concerned back in the summer and that's why Wigan was part of the restrictions that were announced to prevent the borough from seeing the increases that other boroughs have had."
Across Greater Manchester, weekly admissions to hospital for Covid-19 rose week on week from 16 to 35. While there was a drop in the number of patients in ICU beds - from 17 to 14 - those in other beds rocketed from 66 to 103.
More testing is being carried out across the county, with 1,541 tests per 100,000 people last week. Wigan's rate was 1,203 per 100,000, the lowest in Greater Manchester.
Mr Burnham criticised the Government for the timing of its announcements regarding new restrictions and when they are implemented.
He also called for a financial package to support employees and businesses in Bolton affected by yesterday's new rules that pubs and restaurants can serve takeaways only and must close at 10pm.