When Alex Brazier agreed to take part in a three-month polar expedition, he was well aware of the dangers he faced – but a chilly willy perhaps wasn’t the first that sprang to mind.

The 26-year-old doctor is two weeks into a 1,100-mile trek across Antarctica – one of the most inhospitable places on earth where temperatures can go as low as minus 50 degrees.

But it is the nether regions where Alex, a former Junior King’s pupil and the son of Canterbury MP Julian, admits to suffering most.

In an online update about the progress of his team of six military reservists, he writes: “We found that for some reason I was getting particularly chilly in the nether regions.

“There’s a phenomenon called polar penis, which sounds hilarious but as it turns out incredibly unpleasant, and really quite painful and cold, so suffering a bit from this morning.

“Fortunately, I now have a large thick woollen hat stuffed down in that region. It turned out to make all the difference. The hat will probably stay there for the next 80 days.”

Alex and his team are doing the trek unsupported, carrying all their food equipment with them. If they achieve their feat, they will more than double the number of people who have trekked across the entire continent in this way.

Each man is on skis and pulling his own sled, or pulk, across the snow and ice. It contains mostly fuel and food plus their tents.

The trek is being done in memory of Henry Worsley, who died in January trying to cross the continent on his own. The team, known as the South Pole Expedition Army Reservists 2017 or Spear17, is hoping to raise £100,000 for the Army Benevolent Fund.

They constantly have to battle with ferocious winds and cold and routinely suffer from icicles as long as 6in forming off their noses.

On Sunday, team leader Lou Rudd posted this update: “To summarise today, I can probably do it with the word: horrendous.

“Really tough day today for the team, in some difficult conditions.

“We got some advance notice yesterday evening about some strong winds coming our way, and right on cue this morning, as we were preparing during the morning tent routine, the winds really did pick up, and we were faced with about a 45-50-knot head wind which really drove the temperature down as well.

“The wind chill was heading towards the minus 30s and that made going pretty difficult. But we decided to go for it and try and get some progress in, so we packed up, and set off. And then the Great White Queen really started throwing it all at us and fairly soon after we set off.”

Lou says the team considered calling it a day, but instead they persisted and did a full 10 hours – 13.8 nautical miles in distance. They have now passed the earth’s 82-degree point. They are due to finish on January 31.

Log on to www.spear17.org to follow the team’s progress