Ministers have written to the City of London demanding it stop people from swimming in a protected pond on Hampstead Heath, after disturbing scenes of cygnets and eggs being disrupted went viral on social media.

Swans and their 12-day-old cygnets were disturbed by hordes of splashing revellers in the north London park on Monday as temperatures reached a record 35C in the capital. In one video, a swan was seen poking an unhatched egg with its beak after it fell into the water during the chaos.

Conservationists responded with dismay after a video was shared on social media of the scenes, which the local authority, the City of London, called “utterly appalling”.

Coots, moorhens and swans were seen guarding their eggs and young as people obliviously splashed around them. There are large signs around the pond urging people not to swim as it is a wildlife conservation area.

Environment ministers Mary Creagh and Emma Hardy have written a letter, seen by the Guardian, to Gregory Jones KC, the chair of the Hampstead Heath, Highgate Wood and Queen’s Park committee at the City of London.

They wrote that they were “deeply concerned” by the disturbance to wild chicks, adding: “The sight of an adult swan watching an unhatched egg after it fell into the water during the chaos was truly heart-wrenching.”

The ministers asked what steps the City of London would be taking to prevent this from happening again, adding: “As I am sure you are aware, under the Wildlife and Countryside Act 1981, the nests and eggs of all wild birds are protected by law. This makes it illegal, with certain limited exceptions, to deliberately take, damage or destroy the nest of any wild bird while it is in use or being built, or intentionally take or destroy a wild bird’s egg. An individual can receive an unlimited fine and up to six months in prison for each offence if found guilty.”

They said: “We would be grateful to know what steps are being put in place to prevent such an incident happening again.”

Nature charities also criticised the swimmers. The RSPB said it was “a crucial time of year for breeding birds which just want to nest and care for their young in peace”. The bird charity urged people to swim in authorised, lifeguarded spaces rather than nature reserves.