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5 year oldBen Nicholson survived the blast at the Shangri-La Hotel in Colombo but his wife Anita, 42, their son Alex, 14, and daughter Annabel, 11, were all killed.
They had been visiting the country on holiday from their home in Singapore.
Five other British citizens were among those killed in eight blasts.
They include former firefighter Bill Harrop and his partner, Sally Bradley, from Manchester who were also on holiday.
The suicide attacks on churches and hotels in Colombo, Negombo and Batticaloa also left 500 people injured.
Mr Nicholson, a partner with law firm Kennedys, said his family were killed at a table in the restaurant of the Shangri-La Hotel, in the capital Colombo.
He said he was "deeply distressed" at his loss but "mercifully, all three of them died instantly and with no pain or suffering".
He added that his wife, a lawyer for mining firm Anglo American, "was a wonderful, perfect wife and a brilliant, loving and inspirational mother to our two wonderful children".
"Alex and Annabel were the most amazing, intelligent, talented and thoughtful children, and Anita and I were immensely proud of them both and looking forward to seeing them develop into adulthood.
"They shared with their mother the priceless ability to light up any room they entered and bring joy to the lives of all they came into contact with."
He thanked the medical teams in Colombo and the Sri Lankan people he had encountered since.
Assistant County Fire Officer Dave Keelan, of Greater Manchester Fire and Rescue Service, has paid tribute to his former colleague Mr Harrop after hearing the "devastating" news.
"Bill served here for 30 years, retiring at the end of 2012. He was a much a loved and respected colleague and friend. He will be greatly missed."
It is not currently known which explosion killed the couple.
Most of those killed in the explosions are thought to be Sri Lankan nationals but officials say at least 31 foreigners are among the dead including British, Indian, Danish, Saudi, Chinese and Turkish nationals.
Details have started to emerge about some of them, including Sri Lankan celebrity chef Shantha Mayadunne and her daughter Nisanga, and three children of Danish billionaire Anders Holch Povlsen.
The UK's High Commissioner, James Dauris, confirmed that eight British citizens were known to have died but said there were no further Britons with serious injuries.
Mr Dauris said: "We know there are a small number of foreign nationals who are unaccounted for. We don't know what the nationality of those people is."
He urged those still in the country to contact relatives and to follow instructions from local authorities.
Manisha Gunasekera, Sri Lanka's High Commissioner, told the BBC that the large Sri Lankan community in the UK was "very concerned".
The Queen has offered her condolences to Sri Lanka's president, saying her thoughts and prayers were with all Sri Lankans.
She said: "Prince Philip and I were deeply saddened to learn of the attacks in Sri Lanka yesterday and send our condolences to the families and friends of those who have lost their lives."
Three churches in Negombo, Batticaloa and Colombo's Kochchikade district were targeted during Easter services. Blasts also rocked the Shangri-La, Kingsbury and Cinnamon Grand hotels in the country's capital.
Police then carried out raids on two addresses and there were explosions at both. One was in Dehiwala, southern Colombo, and the other was near the Colombo district of Dematagoda in which three officers were killed.
The Sri Lankan government said on Monday that the bombings were carried out with the support of an international network.
It has blamed a little-known local jihadist group, National Thowheed Jamath, although no-one has yet admitted carrying out the attacks.
Police have arrested 24 people in a series of raids.
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