The building has cost more than £500m and the official opening came a decade after its original planned completion date.

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There has also been widespread criticism of its design. Prince Charles described it as looking like "an academy for secret police," while the Labour MP, Gerald Kaufman, said it was as glamorous as a public lavatory.

The official opening had been in the royal pending tray "rather longer than most", the Queen said.

Congratulating the architects, builders, engineers, designers, technicians and management, she said "this labour of love must have seemed at times to be endless".

She described the controversial, modernistic building as "remarkable".

"This is the largest public building erected in Britain this century, and it is entirely fitting that it should be a library," said the Queen.

Accompanied by the Duke of Edinburgh, the Queen toured the £511m building which took 36 years to design and build.

The royal couple viewed the Magna Carta, Jane Austen manuscripts and Beatles memorabilia, including the original handwritten lyrics to I Wanna Hold Your Hand, Help and Ticket To Ride, which are among the 12 million items at the library.

They met some of Britain's leading authors, including PD James, Margaret Drabble, Harold Pinter, Lady Antonia Fraser and the Queen's biographer Ben Pimlott.

The building's design has been critised

The Queen was shown a copy of the Sporting Life from June 8, 1957, featuring a front-page picture showing her leading in her first classic winner at Epsom, Carrozza, which won the Oaks while leased from the National Stud.

Culture Secretary Chris Smith said the new library, next to London's Gothic-style St Pancras Station, was a "magnificent" building which had attracted "just a touch of controversy".

"But many of the critics had now had a change of heart and recognised it as a great architectural achievement," said Mr Smith.

The library, which opened its first reading room last November, is open seven days a week and can be used free of charge.