The council are urging parents to make sure their children have an MMR jab.
It follows an outbreak of measles in south Wales, with fears it could spread to London.
The capital has a lower rate of immunisation take up because of the transient population and high number of people from other countries living here.
In Wandsworth the number of children having the MMR jab dropped to 52 per cent in 2003/4, following the discredited paper linking it to autism.
The rate has since picked up to 80 per cent, but the director of public health, Houda al Sharifi, has warned this is not enough to prevent measles spreading.
She said: "It is clear from what is happening in South Wales how important it is to be vaccinated, and now is the time to do it.
"It’s important that people know what to do with measles and getting immunised.
"Talk to your GP, contact our local immunisation helpline for more information or visit one of our drop in immunisation clinics."
Dr Nicola Jones, chairman of Wandsworth Clinical Commissioning Group, said: "The previous controversy about the safety of the vaccine is now known to be false.
"MMR is safe and will prevent your child from measles infection and the sometimes serious complications it can cause. It is available from your GP surgery."
Parents who want to have their children vacinated or want to double check are recommended to contact their GP.
Alternatively two out of hours clinics are located in St John's Therapy Centre, St John's Hill, and the Balham Health Centre, Bedford Hill.
For more information call the immunisation hotline on 020 8812 6090 or visit wandsworth.gov.uk/fis.