Mrs Cook, who has been comforted by family and friends, was awaiting the outcome of the post-mortem examination today. Her husband collapsed and died while they were hiking on the remote Ben Stack in the Scottish Highlands.
In a statement yesterday, she said: "At this terrible time, I have been deeply touched by the many, many messages of support I have received and Christopher, Peter and I want to thank everyone who has given and offered help.
"I loved and admired my husband more than I can say - for his generosity, his tolerance, his integrity and his great joy in life."
Downing Street indicated that Tony Blair, who went on leave at the weekend, was unlikely to break his holiday abroad to attend the family funeral, but he will attend a later memorial service for the former foreign secretary. The Prime Minister will be represented by John Prescott, the Deputy Prime Minister.
Other senior Labour Party figures who are likely to attend the funeral include Gordon Brown, the Chancellor, who is holidaying in Scotland with his family. Margaret, Mr Cook's first wife, said she hoped to attend, adding: "But obviously I will take Gaynor's wishes into account."
Mr Brown, whose relations with Mr Cook were strained for many years, made it clear yesterday that they had settled their differences and Mr Cook would have been likely to have been brought back into a Cabinet were he to become Prime Minister.
Mr Brown said Mr Cook and his wife had been to the Browns' home in Fife a few weeks ago and discussed his latest book, about public disengagement from the political process. "We were able to smile together at the years of press reports that we never talked to each other," Mr Brown said.
"This was Robin as I'd known him for 30 years: incisive, enquiring, radical and reforming, and always looking to the future, exploring ideas and actions that could change things for the better. I was sure that Robin had much still to do for our country."
Lord Ashdown, the former Liberal Democrat leader, added to the tributes to Mr Cook, praising his commitment to a fairer voting system, and modernisation of Parliament. Constitutional reform had been an "iron in his soul", Lord Ashdown said. "Arguably that will be this Government's most lasting legacy."
Mr Cook's death will lead to a by-election in his Livingston constituency in the autumn. Labour is expected to hold the seat - which Mr Cook last won with a majority of 13,000 - despite a challenge from the Scottish National Party.