Harry Gooby, who spotted and filmed the video of the shark, said at one point the beast appeared to try and come onto the beach itself.
He said: “Its snout came out of the water and onto the beach. It almost nuzzled underneath its neck on the beach.”
‘A real worry’
"Our worry is that it is injured or unwell and might need some medical attention.
"Our advice is to ignore it and give it a wide berth.”
He added: "It could be disorientated and it’s best for our team to monitor it, to give it the space and time to do what it wants.
"It could have just come for a look and will swim off when it’s happy to, but if it’s unwell we don’t want to cause it any more stress by people getting into the water and interfering with it."
How dangerous are blue sharks?
Blue sharks can grow up to 12ft in length and have been known to go for humans and boats out at sea.
They are therefore classified as a "dangerous" species and generally prowl the waters of the Mediterranean, but can also be found in British waters.
What happened to the snorkeller in Cornwall?
A swimmer was bitten by a shark while snorkelling off the coast of Cornwall.
Local media suggest the woman had been out on a blue shark sightseeing trip at the time near Penzance.
Recalling the incident, she said: "I just wanted to say that, despite how the trip ended, it was amazing to see such majestic creatures in the wild and I don’t for a second want this freak event to tarnish the reputation of an already persecuted species.
"I wanted to thank everyone for their amazing actions.
"What was a very scary incident was made so much easier by the kindness and calmness of the people around me.”
She added: "Thank you to the trip team for getting me back to shore quickly and carefully and making me feel as safe as I possibly could.
"We all take these risks when we enter the habitat of a predator and we can never completely predict the actions of a wild animal."
Have other sharks been spotted in the UK?
The attack follows a number of sightings reported along the south coast of England this year, with beach-goers warned to remain vigilant.
In April, pictures emerged of what locals in Plymouth, Devon, believed to be an unusual starry smooth-hound shark.
The species was spotted swimming in a marina yards from a busy tourist spot. The shark is a shallow water variety rarely spotted in the UK.
Meanwhile, photos believed to be of a great white shark were captured by James Venn, 42, while he stood on the beach near Goring, West Sussex, on 4 February.
At the time, Mr Venn told The Brighton Argus: "I went down to the beach to feed the birds when I saw something come up just behind the waves.
"At the time I thought it was a seal but, when I looked at the photos again, I thought it doesn’t look like a seal."
Mr Venn then sent his snaps to experienced shark fisherman Graeme Pullen, 70, who said it was "obviously a shark".
Mr Pullen suggested the fin could belong to a "small, immature great white" that came close to the shore to feed on seals and bass.
However, the claims were later rubbished by harbour experts who said the “fin” was actually a boat part which had come loose.