The Queen of England is depicted as a corgi dog. Elizabeth II is famous for keeping corgis.
Mickey's "one-man band" get up is reminiscent of Bert's from 'Mary Poppins.' The song he plays even sounds a bit like "Step in Time."
To reflect the theme of the episode, the characters all speak with British accents.
This is the second episode that took place in a foreign country (in this case England) where the dialogue is in English instead of another language besides it after "Bottle Shocked". However it's just obvious since Great Britain is already an English speaking country.