Defensive support is described by UK officials as that which aides Saudi air force jets shooting down incoming Houthi missiles and drones.
The singular Voyager aircraft is part of a core fleet of nine – eight military registered and another civilian registered – on the Royal Air Force (RAF)’s books.
The RAF also has five others available for military recall if needed.
Speaking to reporters travelling with him on the way to the United Nations General Assembly in New York, Burnham linked cost of living pressures to the decision.
“I go back to the point I made about cost-of-living pressures and acting to secure the interests of Britain and the wider region,” he said.
“Because of course Saudi Arabia has been experiencing attacks, is looking at potential further disruption, and we need to keep those pathways open, and hence our agreement to the request.”
Shipping routes through the Red Sea are a vital artery of the world economy.
The Houthis recently seized control of the strategic port city of Mokha and Perim Island, a gateway to the Red Sea – a key shipping route used by Saudi Arabia.
In a BBC interview last week, Nato Secretary-General Mark Rutte hinted that European support for Saudi Arabia was likely.
He said: “I would not be surprised if some phone calls were taking place between European allies, ‘hey, how are we going to deal with this?’.
“Let’s see what happens, and if Nato can help, we will always be helpful.”
Energy Minister Martin McCluskey last week told MPs that the UK was “providing air defence support” to Saudi Arabia through the defence partnership that they have, although would not be drawn on questions of operational military activity.
In January 2024, the UK joined the US in launching air strikes against Houthi targets across Yemen.
Then-Prime Minister Rishi Sunak said the UK “acted in self-defence” following the Houthis’ targeting of ships, including a Royal Navy warship.
He also said the strikes were “necessary, proportionate, and targeted” to protect lives and commercial shipping.
Further joint air strikes from the UK and US followed in 2024.