William, Queen Elizabeth's grandson and second-in-line to the throne, and Kate are travelling 1,250 miles across England, Scotland and Wales on board the Royal Train as part of their three-day trip.
They kicked off the tour at London's Euston Station on Sunday evening where they were serenaded by Welsh pop star Shakin' Stevens singing his 1980s hit "Merry Christmas Everyone" before leaving for Scotland.
"Thank you to all transport workers everywhere for keeping the country moving throughout this difficult year," they wrote on a train information board before they set off.
Britain has been the hardest hit country in Europe by COVID-19, with more than 60,000 deaths.
"The Duke and Duchess are very much looking forward to shining a spotlight on the incredible work that has been done across the country throughout this difficult year," Kensington Palace said in a statement.
Queen Victoria was the first reigning monarch to use the Royal Train in 1842, to travel from Slough to London's Paddington station, although critics have questioned its purpose in recent years, saying it is expensive and little used.