The directions The Doctor gives Bill for the wardrobe are the same directions The Ninth Doctor gave Rose in "The Unquiet Dead" (2005).
The last Frost Fair was held in 1814. Dredging of the Thames to make new embankments and the removal of the Old London Bridge increased the flow of the tides, therefore the river could not freeze over as it used to.
The men seen collecting money from people stepping onto the ice would have been the ferry men who lost their income when the river froze over.
The Doctor mentions having been to the Frost Fair "two times" before. In A Good Man Goes to War (2011), River Song mentioned that the (Eleventh) Doctor took her (and Stevie Wonder) to this specific fair, the last one ever held in London, for her birthday. The other time may be the Big Finish Doctor Who story "Frostfire", narrated by Maureen O'Brien as Vicky Pallister, travelling with the First Doctor and Steven Taylor.
According to River Song in 'A Good Man Goes To War,' she and the (Eleventh) Doctor went to this Frost Fair to celebrate her birthday.