One clear problem with setting a game during a specific period of Doctor Who's television history is that the Doctor rarely travels with more than two companions, creating problems for any group with more than three players. Indeed, there are only four points in the history of classic Who where there are more than three regular characters. The first of these occupies the first two seasons, with the Doctor, Ian, and Barbara, plus either Susan or Vicki. The second occurs during the fourth season, when Ben and Polly are joined by a third companion.
In fact, it's interesting to note that this season includes one of the few points where we can definitely say that there must (rather than 'might') be a whole bunch of stories we don't see. Most of the stories in this period end with the beginning of the next one, so that there's no gap at all. But not only is that not true of the gap between The Macra Terror and The Faceless Ones, but, in the first of those stories, Polly gets her hair cut short. By the start of the latter story it's grown back to full length, suggesting a few months have passed at the very least. Who knows where they travelled during that period?
At any rate, with the number of companions having gone back to three again, a new player has obviously joined the group. He comes up with an idea that has apparently never struck the existing players: since this is a time travel game as much as a science fiction one, there is no reason he can't play a character from the past. The character he comes up with is Jamie McCrimmon, a Jacobite piper from the year 1746.