Sarah Applin had given birth to a son just two weeks ago.
When announcing her death, Ms Applin’s parents urged pregnant women and others considered at risk to have the flu vaccination.
Britain’s Health Protection Agency (HPA) says 11 people have died of swine flu in the past week and confirmed the flu has already claimed 47 lives, with three others dying from another strain known as type B.
Most of the deaths were children and young adults, with five deaths among under-fives and eight among those aged between five and 14.
British prime minister David Cameron has admitted parts of the country are now running low on vaccine stocks.
Britain has no central stockpile and vaccines are ordered every year by doctors’ surgeries.
According to the UK Vaccine Industry Group, 14.7 million doses of flu vaccine have been delivered across Britain, which has a population of around 62 million.
Authorities say more than 700 infected people are in intensive care and high-dependency hospital beds.
Hospitals are being told to cancel routine operations to make way for the most seriously ill flu patients.