The comedian's challenge has seen him so far cycle 185 miles from Paris to Calais, where he joined celebrity rowers Davina McCall, Freddie Flintoff and Denise Lewis to cross the English Channel.
Despite suffering from exhaustion, Bishop and his supporters arrived in Dover yesterday evening, completing the second stage of his 290-mile journey.
At 9am this morning, Bishop - said to have been in high spirits - set off on his first marathon, on which he was joined for the first leg by Radio 1 presenter Comedy Dave Vitty.
However, the Liverpudlian took a tumble just a few miles in when his legs buckled. With no injuries sustained, he continued running, and was later joined by presenter Dermot O'Leary.
"I've done around 14 miles so far and I am chaffing!" he said after stopping for lunch. "I should become a spokesperson for udder cream.
"I'm using a whole different muscle group today from the cycle and the row but I am already feeling it. The only problem with running from the coast is that you have to go uphill."
He continued: "Kids from schools have been coming out in fancy dress and people are waving, it's wonderful. It's nice to do something different from rowing this morning but I'm sure the novelty will soon wear off when I have to do it again and again. I keep thinking about the money pouring in and how many vaccinations it will buy and it's keeping me going."
Running on his own, Bishop hopes to finish in Faversham later today. He will finish his third marathon in London's Trafalgar Square on Friday.
Sponsor John Bishop on his 'Week of Hell' by visiting the Sport Relief site.
Take a look at pictures from John Bishop's Sport Relief challenge below: