Mr Brown said in the letter that the outrageous attacks would be met with a vigorous response.
''These outrageous attacks in Mumbai will be met with a vigorous response. I have sent a message to Prime Minister Singh that the UK stands solidly with his government as they respond, and to offer all necessary help,'' the British High Commission here said.
British Foreign Secretary David Miliband, while condemning the attacks, said UK and India would continue their joint efforts to counter the actions of terrorists.
''The attacks in Mumbai which have claimed many innocent victims, remind us, yet again, of the threat we face from violent extremists.
I condemn these attacks unreservedly. Our thoughts are with the families and friends of those killed and injured,'' he said.
British High Commissioner to India, Sir Richard Stagg, visited Mumbai to take stock of the situation.
British Deputy High Commissioner in Mumbai, Mrs Vicki Treadell, and Consular officials have been visiting the injured in the hospitals.
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