The 65 Degrees North team crossing the Greenland ice cap used their IsatPhone 2 satellite phone to update Chancellor of the Exchequer George Osborne on their progress.
The chancellor called the team on the 11th day of their challenge, in which former soldier Peter Bowker, together with four Special Forces veterans and a doctor, is attempting to become the first amputee to make an unsupported crossing of the treacherous ice sheet.
Mr Osborne invited the team to visit Downing Street when they return home.
65 Degrees North, which is raising money for UK charity Help the Heroes, is supported by the Endeavour Fund, set up by the Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry to support sporting and adventure challenges undertaken by wounded, injured and sick service personnel or veterans.
The team is in good spirits despite being hit by a severe weather conditions including energy-sapping winds and heavy snowfall. Covering around 25km (16 miles) a day on skis while pulling a sledge laden with supplies has left Peter with painful blood blisters on his stump.
They are using IsatPhone 2 and Explorer 510 BGAN terminals to stay in close contact with their UK base, update social media and conduct live media interviews, despite being at the outer reaches of the Inmarsat-4 satellite coverage area.
The 600 km (373 miles) journey is expected to take 24-30 days.
