He told passengers on board the Manchester Airport flight to Alicante that he was offering his services as there was no pilot available.
Mr Bradley was filmed by passenger Michelle Potts making the announcement.
The pilot said: "My wife who’s on row 15 with my little boy – hopefully he’s asleep by now, I should keep it down or else I’ll get told off – she rolled over and punched me in the back of the head and said ‘our flight’s delayed by two hours because they are minus one captain for the flight'.
"So just before we went through security I thought I wonder if this is worth a phone call, I think it is because I’d like to go on holiday.
"I phoned up easyJet and said ‘Hiya, I’m standing in the terminal doing nothing. I have got my licence with me and I’d very much like to go on holiday and if you need a favour I’m standing here ready to go."
"This meant customers could get to their destination and shows the commitment and dedication of our crew. This is fully in line with regulations as he had his licence and ID with him. Safety is always our highest priority."