A list of the names of those released, seen by The Telegraph, mentions citizens from other countries including Japan, Australia, the Czech Republic and Finland.
On Wednesday, Joe Biden, the US president, claimed success in securing the safe passage of US nationals and others.
He said: “Today, thanks to American leadership, we secured safe passage for wounded Palestinians and for foreign nationals to exit Gaza. We expect American citizens to exit today, and we expect to see more depart over the coming days.”
The delays and confusion over evacuations are believed to be down to careful vetting and a delicate deal between Israel, Egypt and Hamas.
The Israel Defense Forces said Israeli intelligence was vetting all foreign nationals leaving the Gaza Strip for links to terrorism before allowing their names to be included on the release list held at the Egyptian border.
The Israeli veto on names could cause tension with allies over the next days and weeks if some foreign nationals are prevented from leaving.
The evacuation of British nationals is expected to take place in stages and over several days, with Israeli and Egyptian authorities to determine who is allowed to cross and when. Civil servants have provided a full list of names of UK nationals and dependents in Gaza to both sets of authorities.
Celebrating the news of the first British citizens to escape, James Cleverly, the Foreign Secretary, said: “The first British nationals have left Gaza. This is a hugely important first step.
“We are working with Egyptian and Israeli authorities to ensure the crossing stays open so all British nationals can get to safety in the coming days.”