Four Britons were injured in the attacks, three of whom are being treated in hospital, No. 10 said.
Mr Dixon’s family and friends have appealed for information on social media after he failed to turn up for work following the attacks.
The IT programmer, who lives in Brussels and is originally from Hartlepool, was travelling to work, but did not arrive at his office. He is pictured above with his partner Charlotte Louise Sutcliffe.
A No. 10 spokesman said: “We are concerned about one missing British national and we are in close contact with the Belgian authorities.
“We are aware of four British nationals who were injured in the attacks. Three are being treated in hospital, one has already been discharged. Our embassy staff are working to assist all British nationals affected.”
‘Alert and vigilant’
The spokesman said the government was no longer advising British people to avoid travelling to Brussels, but “British nationals in Belgium should remain alert and vigilant, stay away from crowded places, and follow the instructions of the Belgian authorities”.
Security has been increased in the UK following the attacks at Brussels airport and the city’s metro, in which 34 people died.
“Here in the UK, we stepped up the security presence at a number of locations across the country yesterday and we will maintain this in the coming days,” said the spokesman.
“The national threat level remains at severe (an attack is highly likely) and the public are advised to be ‘alert but not alarmed’.”
The first confirmed fatality was mother-of-two Adelma Tapia Ruiz, 37, from Peru. She was killed at Brussels airport, along with 13 others.
Her Belgian husband, Christophe Delcambe, and their twin four-year-old daughters Maureen and Alondral survived.
Another 20 people died on the Brussels metro in attacks claimed by Islamic State.