But for 10-year-old Hannah Thomas it really did happen. It was during a dance lesson at Oriel primary school in Hounslow, west London.
"Are you Hannah?" asked the stranger as he walked into the room. "We're Blue - we've come here to see you."
While the Year 5 pupil gasped in awe, two more members of the chart-topping boy band sauntered into the lesson and presented Hannah with a bunch of flowers.
Several weeks earlier, Hannah had entered a competition organised by the BBC's Top of the Pops in which the winner would get to meet the band.
After receiving no response, Hannah had presumed that the prize had gone to some other lucky youngster. However, the programme's producers had secretly contacted Oriel's headteacher, John Stephens.
"It was all very hush-hush," said Mr Stephens.
"We smuggled the band in and hid them in the nursery. They liked all the equipment there, and were particularly taken with the stuffed animals."
Blue, who have had seven top-10 singles and three number one hits, spoke to all the pupils in the Year 5 group before retreating to spend some time with Hannah.
"It was brilliant," she said. "I asked them what it was like to be a pop-star, and we talked about the bands I like, though one of them spent most of the time on his mobile phone."
Later some of the older pupils joined the band in the school hall to watch them perform their forthcoming single "Breathe Easy".
BBC cameras were there to record the performance in front of the screaming uniformed fans for broadcast on an upcoming edition of Top of the Pops.
"The dinner ladies all came in to watch and the teachers were waving their arms and dancing," said Hannah. "That was weird. We should have pop-stars in school every week."
She is now relishing the envious glances of her classmates.
Ten-year-old Clare Barnes said: "I felt very jealous of Hannah. I'd have liked to talk to Blue on my own. But I didn't tell her.
"I'll just enter competitions from now on."
Highlights of Blue's visit to Oriel primary along with their performance of "Breathe Easy" will be screened on Top of the Pops on Saturday, March 27