Tickets for the David Bowie tribute concert and First Night Of The Proms sold out in just over an hour after BBC Proms tickets went on sale on Saturday morning.
The Royal Albert Hall revealed it had sold out in a message on their live-blog at 10:06am and apologised to fans who were still in the queue, with a further nine events selling out in the course of the morning.
Disappointment for music lovers who were not able to get their hands on the coveted tickets was quickly compounded when tickets began appearing on re-sale websites for many times their original value.
Official tickets for the Bowie prom were banded from £10 to £35 but soon appeared for as much as £187 for a ticket in the circle with a restricted view.
A seat in the stalls for the First Night Of The Proms - less than £48 through the Proms website - was on offer for £182.55 through website Viagogo.
One angry user tweeted: "This should not be allowed!"
Another fumed about missing out on a seat, writing: "Well done! Great system."
A BBC spokeswoman said it was an "industry-wide and serious problem" and tickets may be refused if they have been re-sold.
She said: "The Royal Albert Hall is the only official ticket seller of the BBC Proms. The resale of tickets bought from the Royal Albert Hall Box Office is against the Hall's terms and conditions. Where it's possible to identify customers, appropriate action will be taken.
"Reselling a ticket makes it void and the ticketholder may be refused entry. Whilst we use no other ticket agent it is very difficult to manage unofficial selling. This is an industry-wide and serious problem and we work closely with the Royal Albert Hall to do what we can to prevent this."
Ticket buyers did, however, praise the online system, which saw them move swiftly through a queue of more than 10,000 people.
One wrote: "Quickest ever ticket buying for @bbcproms - well done @RoyalAlbertHall system!"
Another added: "I must say that #BBCProms booking system is very efficient. I have moved up more than 5,000 places in the queue in the space of 35 minutes."
The BBC Proms run from July 15 to September 10.