Only 13 of the 1948 Gandhi 10-rupee Purple Brown and Lake 'Service' stamps are in circulation.
The block of four was sold to a private collector-investor in Australia for the highest ever price for Indian stamps, said dealer Stanley Gibbons.
However, the record price for a stamp sold an auction was $9.5m (£7.4m).
That British Guiana one-cent magenta stamp was sold to an anonymous bidder in June 2014.
The Indian stamps were particularly rare owing to the fact they were in a set of four.
Stanley Gibbons previously sold one of these singles for £160,000 to a client in Uruguay last year.
A block of four is in the Queen's stamp collection, which is believed to be the world's largest and most valuable in private hands.
Keith Heddle, managing director of investments at Stanley Gibbons, said: "The market for high-quality Indian rarities has been strong for several years and is supported by the ongoing desire of the wealthy Indian diaspora and savvy international clients to own these historic assets."

His villainous character Ethan Rayne was the arch enemy of regular character Giles, played by Anthony Head.
The London-born actor also played the evil General Sarris opposite Tim Allen in Galaxy Quest.
His ex-wife Casey Defranco called him "a wonderful person, extraordinarily talented as an actor."
Staff on his official website wrote: "Please join us in raising a glass to Robin - goodbye, dear friend. Thank you for all the laughter and the cookies. We will miss you so very much."
Sachs' first role was with the British Hammer film studio, in the movie Vampire Circus.
He went on to play Adam Carrington in the 1991 miniseries Dynasty: The Reunion when the original actor Gordon Thomson was unavailable.
Sachs worked on several sci-fi shows, with appearances in Babylon 5, Star Trek: Voyager and Torchwood: Miracle Day.
His stage work included touring productions of Hamlet and Twelfth Night.
In 1999, he appeared heavily disguised under layers of heavy make-up as the baddie Sarris in the satirical comedy Galaxy Quest, which co-starred Sigourney Weaver and Alan Rickman.
Later in his career, Sachs provided voices for several video games including Mass Effect 2 and 3 and Resident Evil Damnation.

US officials described the intercept by the SU-27 jet on Wednesday as "dangerous and unprofessional".
Russia's defence ministry said the US plane had been approaching Russian territory and the SU-27 pilots had adhered to international rules.
Russia is currently carrying out military exercises in the Black Sea.
Pentagon spokesman Capt Jeff Davis said the US Navy P-8A Poseidon aircraft had been conducting routine operations in international airspace when the Russian fighter made the unsafe manoeuvre.
"These actions have the potential to unnecessarily escalate tensions, and could result in a miscalculation or accident," he said.
A US defence official quoted by AFP news agency said the Russian plane had flown within 30ft of the P-8A before closing to just 10ft.
However, the Russian defence ministry said fighters intercepted the US plane because it was heading towards Russian territory with its transponder signal - which helps others identify it - switched off.
"After the Russian fighters got close to the spy planes for visual confirmation and to determine their wing numbers, the American aircraft changed course sharply and flew away," a statement said.
"The Russia pilots acted in strict accordance with international rules for flights."
Relations between Russia and the West have been strained since the Russian annexation of Crimea from Ukraine in March 2014.
In April, the US complained that Russian jets had confronted one of its reconnaissance planes over the Baltic Sea in an "unsafe and unprofessional manner".
In that incident, Russia also said that the US plane had turned off its transponder signal.
A set of four stamps featuring the portrait of Gandhi has been sold for £500,000 - but the total remains well short of an international record.
[NEXT_CONCEPT]
British actor Robin Sachs, best known for his role in the hit TV series Buffy The Vampire Slayer, has died at the age of 61.
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The Pentagon says a Russian fighter plane flew within about 10ft (3m) of one of its reconnaissance aircraft operating over the Black Sea.