Re: Yes, but...
Yes because Shoreditch and Canary wharf are sooooo far away from Central London.
7 stops on the Jubilee line gets you from Westminster to Canary Wharf.
9 Stops on the Circle/District line gets you to Liverpool Street which coupled with a 10minute walk gets you to Shoreditch high street.
So maybe 20 minutes travel time total. Considering that no one below the rank of Executive lives within 5km of Westminster and as such your average workers are already coming from somewhere else in London, which probably has better connections to Liverpool Street/Shoreditch or Canary Wharf, then I doubt you would see a mass exodus as if you were moving to say Royal Tunbridge Wells (for example).