Chloe Buckley, from north west London, and Bedfordshire GP, Dr Michael Day, died after suffering from the virus. Their deaths took the number of UK deaths linked to swine flu to 17.
On Monday health bodies, the British Medical Association (BMA) and the The Royal College of General Practitioners, urged the public not to panic.
Chloe died last Thursday at St Mary's Hospital in Paddington. A post-mortem is due to be carried out to determine if she had underlying health conditions.
Dr Day died on Saturday in the Luton and Dunstable Hospital. A subsequent swab test revealed he had swine flu although it is not yet known if this was the cause of his death.
Health Secretary Andy Burnham said the UK was well placed to deal with the outbreak but could not rule out further deaths.
He said: "Although the swine flu virus is proving generally mild in most people, in some cases it is more severe. Unfortunately, as with seasonal flu, people may develop complications and in some cases will die."
The first British patient without underlying health problems died on Friday after contracting swine flu. The patient, from Essex, died in Basildon.