The Queen has written to the King of Norway to express her shock and sadness at the attacks in his country, Buckingham Palace said.
She said her and the Duke of Edinburgh's thoughts were with the Norwegian people.
Her message to King Harald read: "I am deeply saddened and shocked by the tragic loss of life of so many people on the island of Utoya and in Oslo.
"Prince Philip joins me in extending our heartfelt sympathy to Your Majesty and the people of Norway. Our prayers and thoughts are with everyone who has been affected by the dreadful atrocity."
Members of the public in Britain also voiced their solidarity and sympathy, posting messages of support on the Facebook page for the Norwegian Embassy in London.
Paul Rawnsley wrote: "The love and thoughts are with you from all of Britain. Such a beautiful people and country. Never change. All peaceful and freedom loving people are standing shoulder to shoulder with you."
Another user of the social network site wrote: "How sad I am to hear such an evil has been committed on such a peaceable nation! The thoughts and prayers from the people of England go out to you all."
And Nicola Flynn said: "My condolences to all those who have lost loved ones. The world is watching in sympathy as your people try to recover from this, we know in Britain what a truly great and dignified nation Norway is and our thoughts are with you."
The Royal Norwegian Embassy in Belgrave Square, central London, is open, its flag flying at half mast.
A spokesman said: "We're open for any Norwegians who might need someone to speak to or feel the need to be with someone."