The musicians all have an estimated wealth of more than £150m after successes in the UK and US.
But they are not quite moneyed enough to make the main Rich List where people must boast wealth of £350m or more.
That includes UK Prime Minister Rishi Sunak and his wife Akshata Murthy, though their wealth has fallen.
For those under 35, Ed Sheeran, 32, is ranked the seventh wealthiest with a fortune of £300m, helped by his fast-selling sixth album "Subtract".
Adele, who is now 35, is in ninth place with £165m. The London-born singer has sold more than 100 million albums, and earlier this year she announced that her lavish Las Vegas residency would be extended. Reportedly, this pays £500,000 per show.
Harry Styles had the biggest-selling UK album last year with "Harry's House", and is currently on tour in the UK. The 29-year-old's wealth is pegged at £150m.
Sitting on top of the main Rich List is Gopi Hinduja and family, who own a vast conglomerate of businesses across the world and whose combined wealth is £35bn, up from £28.4bn last year.
Sir Jim Ratcliffe makes a return to the top 10 of Britain's richest people after two years down the ranks.
Now worth £29.6bn, Sir Jim is perhaps best known at the moment for his battle to buy Manchester United, his football team since boyhood. He made his fortune through Ineos, a chemicals and raw materials business.
While the Rich List is made up of the uber-wealthy, this is the first year that the number of billionaires has fallen since the global financial crisis in 2008 when the banking industry nearly collapsed.
There are now 171 billionaires listed, down by six from the previous year. The economic impact of Covid, high inflation and rising interest rates - which make it more expensive to borrow money - have weighed on the fortunes of the rich.
Sir Richard Branson, who recently told the BBC he feared losing everything during the pandemic, has seen his wealth almost halve to £2.4bn. The man behind the airline Virgin Atlantic said he lost £1.5bn as Covid lockdowns grounded flights and kept his hotels and health clubs shuttered.
Mr Sunak and his wife Ms Murthy have also seen their fortunes fall by £200m, from the £730m they were worth last year to £529m.
The majority of their wealth comes from Ms Murthy who owns a sizable stake in her father's IT business Infosys.
The newly-crowned King Charles III has the relatively low ranking of 263 on the Rich List with a fortune of £600m. However, he is wealthier than his late mother, Queen Elizabeth II, who was worth £320m, according to last year's list.
Considerably richer is JK Rowling, the author of the Harry Potter books. She is worth £875m, a rise of £25m from the previous year. She could become wealthier still - the writer is reportedly in talks with the TV network HBO about making her most famous creation into a series.
Meanwhile, two of the stars of the Harry Potter films are on the list of the richest under 35s. Daniel Radcliffe, 33, is worth £92m while Emma Watson, also 33, has an estimated wealth of £60m.