A further 145 patients were confirmed with swine flu in England today, taking the UK total to more than 1,750, health chiefs said.
An additional 22 cases were confirmed in Scotland yesterday while three have fallen ill in Northern Ireland.
Jacqui Fleming, 38, of Glasgow, became the UK's first swine flu victim to die on Sunday, two weeks after giving birth.
Her son, named Jack, died in hospital in Paisley, Renfrewshire, on Monday night.
After revealing the number of cases in the UK had now reached 1,752, a Department of Health spokesman said: "The localised cases of swine flu found in the UK have so far been generally mild in most people, but are proving to be severe in a small minority of cases.
"We are continuing to work to slow the spread of the disease and to put in place arrangements to ensure that the UK is well-placed to deal with this new infection."
Last night, a statement from the Crown Office confirmed Ms Fleming died from swine flu.
It said: "The death of a 38-year-old woman, Jacqueline Fleming, at the Royal Alexandra Hospital, Paisley, on June 14 2009 was reported to the Procurator Fiscal at Paisley.
"With the agreement of her family, we are able to confirm that the cause of death has been certified as multi-organ failure due to influenzal pneumonia (H1N1)."
Ms Fleming lived with her two other children - one aged 18 and one of primary school age - and her long-term partner in the family home in Carnwadric, Glasgow.
The mother had been in intensive care at the Royal Alexandra hospital.
Hers was the first death to be reported outside the Americas where at least 145 people have died from swine flu.
Her family said in a statement on Monday it was "devastated" by the loss.
Professor Hugh Pennington, a bacteriologist at Aberdeen University, said the first swine flu death was not unexpected.
He said: "It does not point to the virus getting nastier. All the evidence to date suggests the virus is not changing at all."