Mustique is an idyllic hideaway in the Caribbean, a millionaires' playground where Princess Margaret and Mick Jagger own holiday homes. Mr Dennis, the ex-hippie turned publishing magnate, has a pied a-terre there that once belonged to David Bowie.
Eigg, population 70, is a scrap of land in the Scottish Hebrides famous for its rugged scenery and bracing climate.
Mr Dennis, a defendant in the 1971 Oz magazine obscenity trial, has taken an interest in Eigg since residents clubbed together to buy the island last year. He offered to fund the exchange after donating computers to the local school.
In April, three children flew to the Caribbean, where they revelled in the sunshine, warm seas and exotic food. This week it was the turn of four of their counterparts to visit Scotland. The party stopped off in London to buy socks and warm jumpers, which are not available on Mustique.
It was a wise move. Eigg is experiencing one of the coldest summers of recent memory and has had drizzling rain and overcast skies this week.
"One child was frozen solid when she arrived off the ferry," said Maggie Fyffe, secretary of the Isle of Eigg Heritage Trust, which owns the island.
Godwin Martin, the schoolteacher who accompanied the children on their two-week visit, is intrigued by the novel climate.
"It's cold, even when the sun comes out," he said yesterday. "When the sun shines in Mustique, it's hot."
But the Caribbean children do not feel that they have had a raw deal. They are enjoying the change of scene and have adapted swiftly to their new surroundings.
In past days, they have been on a trip to the neighbouring island of Mock and gazed at seals and seabirds in a wildlife sanctuary. They also had a picnic in the gardens of the Lodge, home of the former lairds of Eigg.
Eleven-year-old Shaundy Charles, one of the Mustique party, declared himself delighted by the Hebrides. "It's cold, and it's different from Mustique, but it's nice," he said.
The adults are in no doubt about who got the better half of the exchange. "It was an amazing opportunity for our children," said Mrs Fyffe, barely restraining a fit of giggles.
In fact, there are a surprising number of similarities between the two islands. On both, the children have to go away to secondary school.
The Caribbean pupils have to go to the island of St Vincent, the Scots to Mallaig on the mainland, or to Skye. Both places rely on private generators for power.
And there are, implausible though it seems, palm trees on Eigg, thanks to the warming influence of the Gulf Stream.
And Mr Dennis? Currently spending a couple of weeks on Mustique. He is, Mr Martin confirms, a "mightily humorous" man.Reuse content