Almost 50 more deaths were recorded in Cornwall in June than a year ago as lockdown was eased in England, official figures show.
A new report is calling for "intense preparations" to ready the NHS for winter, with fears a second coronavirus wave could lead to 120,000 deaths nationally.
Office for National Statistics figures show 502 deaths were recorded in Cornwall during June.
That was 49 more than the number recorded in June 2019, a rise of 11 per cent.
This was higher than the average rise across the South West's 30 local authorities, where death counts increased by seven per cent.
It means that in the year to the end of June there were 327 (10 per cent) more deaths in Cornwall than at the same point last year.
Across England and Wales, 332,734 deaths recorded were recorded between January and the end of June, an increase of 62,640 on the same point in 2019.
But the official coronavirus death toll on July 3 from the ONS was only 50,813.
Dr Chaand Nagpaul, British Medical Association council chair, said: "These figures show that while attention has focused on mortality figures from coronavirus, there has been a disturbing hidden impact of the pandemic on millions of people who were unable to access care and treatment during the pandemic.
"Our overstretched NHS simply did not have the capacity to deal with Covid-19 patients as well as continue to provide care for non-Covid patients."
The BMA said it estimates 1.5 million fewer operations and treatments took place over the last three months compared to the average in the past two years.
A Royal Academy of Medical Sciences report has warned there could be 120,000 coronavirus deaths in UK hospitals in a reasonable worst-case scenario this winter, with the NHS expected to struggle with a backlog of patients and a possible flu pandemic.
The estimate, which excludes care home deaths, is based on the Government taking no action, with the Academy calling for urgent and intense preparation now to ready the NHS.
Professor Stephen Holgate, who chaired the report, said: “This is not a prediction, but it is a possibility. The risk of this happening could be reduced if we take action immediately.
“With relatively low numbers of Covid-19 cases at the moment, this is a critical window of opportunity to help us prepare for the worst that winter can throw at us.”
The report calls for increased capacity in the test and trace programme, a campaign to encourage flu jabs for vulnerable people and health workers, and efforts to stock PPE.
The Department for Health and Social Care said it will ensure all necessary preparations are in place to avoid a second peak that would overwhelm the NHS.
A spokeswoman added: "This includes extensive winter planning, expanding our testing capacity even further, working intensively on new treatments, providing the most comprehensive flu vaccination programme in the UK’s history, and delivering billions of items of PPE to protect our health and social care workers."
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