The Regency era was a time period in the United Kingdom during George IV's reign.
The First Doctor, Steven Taylor and Vicki Pallister visited the River Thames frost fair on February 1814, which Vicki described as the "last great frost fair". (AUDIO: Frostfire) The Eleventh Doctor, River Song and Stevie Wonder visited the same fair for River's birthday in 1814. Wonder performed for them in private, under one of the bridges. Given his blindness, Wonder was unaware that he had travelled in time. (TV: A Good Man Goes to War)
The Twelfth Doctor also visited Regency London with Bill Potts, where they attended the same frost fair and investigated people disappearing on the ice, which turned out to be a giant sea serpent. Lord Sutcliffe planned to blow open the ice during the fair, enabling the serpent to feed on them all. However, the Doctor placed the explosives next to the creature, freeing it from its chains. When Sutcliffe went onto the ice to investigate, the serpent cracked the ice, and Sutcliffe fell through. (TV: Thin Ice)