Mr Fairbrother, an oak merchant, is hoping to break the world record for the “fastest marathon carrying a household appliance (white goods)”.
He says Hertfordshire Police officers quickly realised he was not a fridge thief and added that he admired their diligence.
The father from Stevenage said: “It was pitch black and night time. A police car passed me very slowly, I had a gut feeing they didn’t like what they saw and they spun around and pulled over next to me. Their blue lights illuminated and all traffic stopped.
“I was red faced and embarrassed, I thought ‘are they going to believe me?’ are they going to think I’ve knicked the fridge?
“They said: ‘Is that a fridge on your back?’
After Mr Fairbrother explained his 26-mile challenge, he said the officer joked: “You do know if you order from Currys, they will deliver it for you?”
Mr Fairbrother says the officer wound down his window to shake his hand and wished him good luck.
He added: “I’d be more worried if they saw me with a fridge on my back and didn’t stop to investigate. It was really funny.”
So far, the keen fridge-runner has raised £4,284 of his £10,000 target.
Mr Fairbrother explained that he only started running two and a half years and has since run half marathons, marathons and even ultra marathons.
The record for the fastest marathon holding an appliance stands at four hours, 53 minutes and 10 seconds and he was inspired after seeing a marine break the world record in the news last year.
He added: “Sam is the first person I knew with diabetes and I didn’t know how it affected people. I’m not a doctor and I’m never going to cure diabetes but I can go and do stupid things to raise money for it.”
Mr Fairbrother’s world-record feat was nearly foiled at the first hurdle when he initially was not given a place to run the London marathon with Diabetes UK.
After his rejection in July he contacted the charity who put him at the top of the reserve list.
In December, he got the call he had been hoping for.
He added: “Obviously I’ve missed out on some training and I’ve had to adapt my running style.
“The main thing is I’ve managed to stay injury free and I’m determined to stay there.”
The marathon runner has named the fridge Tallulah after the Cool Runnings bobsleigh and has documented his progress on his Instagram and TikTok handle @c00lrunnins.
He does three shorter runs in the week and one longer run at the weekend, with his unusual companion.
He added: “At first I could tell people would see me and think what is he doing.@
“Thanks to the publicity, now I have overwhelming support and people stop to beep their horns and cheer me on. It’s amazing.”