Sir Bradley Wiggins has left the Giro d'Italia to return home to recover from the severe cold and chest infection that ruined his hopes of winning the first Grand Tour of the 2013 season.

He had been lying 13th overall, but the writing was clearly on the wall when he was left behind by the peloton during Thursday's rain-soaked stage into Treviso, losing three minutes.

"We monitored Bradley overnight and this morning we've withdrawn him from the Giro after consulting the team doctor," the Team Sky head, Dave Brailsford, said on Friday. "His chest infection has been getting worse and our primary concern is always the health of our riders. Bradley will return to the UK today for treatment and to rest and we hope to have him back on the road as soon as possible.

"As a passionate racer he wanted to continue but he is simply unable to do so on medical grounds."

Team Sky had said that a decision would be taken first thing on Friday depending primarily on Wiggins's health but also on the weather, as further rain would be certain to affect him adversely. Rain was forecast for Friday morning in Emilia Romagna, the location of the stage start, together with winds gusting to 40km/h.

The risk was that by continuing to pursue what had become a lost cause, Wiggins might create more problems for his health in the long term. A prompt withdrawal at least means he can return for the Tour de France; there are opportunities for him to return to competition before then, including the Tour of Switzerland in late June, but the team will wait for a complete recovery before deciding on his programme.

Wiggins had made the sign of the cross to cycling fans at the finish of Wednesday's stage in Fruili; even though he was able to hang on to the leaders, he admitted that he had been ill for several days and had been taking antibiotics. He had limited his time loss on the first severe mountain-top finish of the race on Tuesday to just 37sec, inspiring hopes that he might still tilt for the podium.

The most likely cause for Wiggins's sickness is the rough weather which has followed the Giro as it has travelled from the south of the country to the north. While some cyclists thrive in the wet and cold, Wiggins has always been open about the fact that he is susceptible to such conditions.

The wet weather hit the Giro 10 days ago, on stage four, and Thursday was the fourth stage run in rain and cold; Wiggins had lost time on stages four and seven in the grim conditions. The forecast for the weekend's Alpine stages is for snow, with speculation that Sunday's finish on the Galibier will be cut short.

Wiggins was not the only winner of a Grand Tour from 2012 to quit the race; before the Briton's departure was confirmed, Garmin-Sharp announced that Hesjedal would not start Friday's stage. The Canadian had suffered immensely on Tuesday's stage in Friuli, and like Wiggins, the three-hour run on to the Veneto plains on Thursday proved too much for him.

"There's a virus that's been going around, so it could be that, or severe allergies – whatever it is, I'm only getting worse," said Hesjedal in a statement released by his team. "Yesterday's stage was just too much for me, I fought to get through it but after seeing the medical staff last night, I also know that its time for me to go home, get some tests done and get healthy again.