They also found almost one in five tickets for Lady Gaga and 15 per cent of tickets for the first night of the BBC Proms at the Royal Albert Hall were listed for sale on secondary sites.
Hundreds or even thousands of tickets appear on the four main resale sites - Viagogo, StubHub (owned by eBay) and GetMeIn or Seatwave (both owned by Ticketmaster) - as soon as any major event goes on sale.
The Competition and Markets Authority (CMA) is now investigating suspected breaches of consumer protection law in the secondary ticketing market. The tickets discovered on those sites will no longer admit fans to the shows.
Tickets for the first night of the BBC Proms with an original cost of £38 were found to have a mark-up of 279per cent on StubHub (£144) and 300per cent on GetMeIn!
Which? also found consumers are still not getting the ticketing information required by law when buying from secondary websites.
Commenting on that work in the Daily Record, Mike Andrews of National Trading Standards said: "We know fans desperate for tickets will often pay hugely inflated prices to get them from unofficial ticket sellers, and next year's Ed Sheeran tour has proved to be no different".
'There needs to be more transparency within the secondary ticketing industry and the competition authorities must take strong action against those who aren't playing by the rules'.
A Which? investigation has found that up to one in four tickets to popular events are now on rip-off ticket websites.
Many people carry out a simple Google search to find tickets, only to find Viagogo, GetMeIn, Seatwave and StubHub appearing at the top of search results, with little to distinguish them from primary ticket agents.
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StubHub claims the real issue is tickets held back for the industry, VIPs and other sellers.
At the 6 Music festival, tickets for Depeche Mode who played the 2,100-capacity Glasgow Barrowland were sold out in minutes with £30 briefs immediately becoming available on the Viagogo ticketing resale site and selling for up to £879 each.
Viagogo's charges are particularly steep - the site adds as much as 34% in fees - and you don't see the full VAT-inclusive price until you click through to add payment details. The seller of these tickets is not known, as Viagogo protects their identities.
Ticketmaster told Which? that the number of tickets sold on its resale platforms (GetMeIn and Seatwave) makes up a very small proportion of its overall sales.
They found 26 per cent for a show by comic Jack Whitehall were being offered by secondary sites a day after going on public sale.
A spokesman said: 'We have always championed transparency and consumer protection, and pride ourselves on ensuring compliancy with all rules and regulations.
It said: 'The problem with access to tickets doesn't lie with the secondary ticketing market - indeed, your findings show that only a small percentage of tickets end up here - but is due to the fact that not all tickets are available to the general public'.
Which advice on how to avoid being ripped off • Sign up for ticket alerts: Join fan clubs and mailing lists of your favourite artists, festivals, venues and primary ticket sellers for reminders of when tickets go on sale.
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