One of the greatest advantages a TARDIS had over any other kind of transport vessel was that there was almost unlimited space inside.
"Everybody in!" the Doctor called over the blaring of alarms, directing a steady stream of people through the open door. "No need to push, there's plenty of time to get you all safely aboard."
"But how will we fit?" one woman asked. "Won't we get crushed?" Two small children were clinging to her skirts and they were clearly the source of her concern.
"Not at all." The Doctor smiled reassuringly. "Lots of room; you couldn't be safer."