The man was arrested on Tuesday evening on suspicion of Computer Misuse Act offences and has been released on bail
The BBC has seen an internal memo sent to airport staff at Heathrow about the difficulties software provider Collins Aerospace is having bringing their check-in software back online.
The company appears to be rebuilding the system again after trying to relaunch it on Monday.
The US firm has not put a timeline on when it will be ready and is urging ground handlers and airlines to plan for at least another week of using manual workarounds.
At Heathrow, extra staff have been deployed in terminals to help passengers and check-in operators but flights are still experiencing delays.
On Monday, the EU’s cyber-security agency said ransomware had been deployed in the attack.
Ransomware is often used to seriously disrupt victims’ systems and a ransom is demanded in cryptocurrency to reverse the damage.