The 80-year-old retired Atomic Weapons Establishment scientist, of The Green in Tadley, has been described by his neighbours as a "wonderful man".
Local residents told the BBC he kept himself very physically fit having undergone heart surgery.
Tadley Town Council Chairman David Leeks said the reaction in the town was one of "pure shock".
He said: "We had a meeting last night and it was mentioned.
"We found it very difficult to believe that someone from Tadley had suffered this way.
"You don't expect something like this to happen in your community.
"Our thoughts go out to his family".
Neighbours said Mr Thompson was a keen walker who was known to do up to 60 press ups a day and loved holidays.
The BBC understands his long-term partner is currently staying with family.
Tadley Town Council will hold a minute's silence outside its offices on Friday.
The family of Mr Thompson issued a statement via Hampshire Constabulary, which stated: "We understand the interest the media has at this time, but we do not wish to be approached by nor speak to any members of the media.
"We ask that you respect our privacy and our wishes at this extremely difficult time."
The police force told the BBC the family have confirmed the death to the Foreign Office, and have been given a family liaison officer.
Twenty-one Britons have been identified as victims, with nine more believed to among the dead, Downing Street said.

Mr Rouhani ordered a review of all 3,000 jobs on offer, and a rethink if they were found to be biased to men.
Some departments, such as the Judiciary Organisation of Military Forces, which is controlled by hardliners, are open almost exclusively to men.
Mr Rouhani has a track record of speaking out on women's rights.
He has appointed a number of women to prominent posts - including Masoumeh Ebtekar as vice-president and head of the Environmental Protection Organisation, and Marzieh Afkham, who was foreign ministry spokesperson, before being appointed ambassador to Malaysia last year.
Ms Afkham was the first woman to be made a foreign envoy.
After Iran's parliamentary elections in May, Mr Rouhani hailed the record number of women who won seats.
But civil society groups say he could have done much more to tackle the overall problem of female unemployment.
Iranian women have made big progress in education in the decades since the Islamic Revolution in 1979, and now make up 60% of all university graduates. However, they are still significantly under-represented in the workplace.
The most recent figures from the Iranian National Statistics Organisation in 2013 revealed that just 12.4% cent of Iranian women were in active employment.
Young Iranian women are five times more likely to be unemployed than young men, and twice as many women than men have lost their jobs as a result of the economic downturn caused by international sanctions.
Women face the double challenge of deeply entrenched conservative values plus discrimination enshrined in a legal system, which disadvantages them in many areas including marriage, maternity provisions, custody rights, and even the right to travel.
In the past 12 months a number of high-profile scandals have highlighted the very real problems many women face in their everyday working lives.
In September 2015 the captain of the Iranian women's football team, Niloufar Ardalan, was reportedly unable to take part in a key international match because her husband had refused to give her permission to leave the country.
And in February secret recordings of a senior manager at the state broadcaster making suggestive phone calls to a junior, female employee put the spotlight on sexual harassment in the workplace.
President Rouhani's championing of women's rights has sometimes put him at odds with Iran's Supreme Leader, Ayatollah Khamenei, and the conservative establishment, which favours a more traditional and restricted role for women, with the emphasis on motherhood and home.
The government has invested in job creation schemes in recent years, but critics say much of the money has been channelled into male-dominated sectors of the workforce, resulting in even greater shortages of jobs for women.
One of the Tunisia beach attack victims has been named locally as David Thompson from Hampshire.
[NEXT_CONCEPT]
Iranian President Hassan Rouhani has postponed the annual civil service entry exam because of concerns it discriminates against women.