Staff at the Queen Victoria Hospital's specialist burns unit said they had treated 13 children for severe sunburn since the start of June.
A further 18 children had required specialist treatment for barbeque related burns.
Consultant plastic surgeon Nora Nugent said the burns unit was treating an unexpectedly high number of cases.
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'Cool, call and cover' - first aid for burns
She said: "No parent intends for their child to get sunburnt and accidents do happen."
She urged people to apply sunscreen and to keep children away from hot coals.
Most of the barbeque injuries had happened while children were playing near a barbeque that was in use or had not cooled down, she added.
The East Grinstead hospital is known for its history following the work of Archibald McIndoe who treated badly-burned World War Two servicemen.
It remains a leading centre for burns and reconstructive surgery.
Specialists have treated a one-month-old baby for severe sunburn at a unit in Sussex, prompting safety warnings.