Possibly part of A Series-Ful Of Plots, Series Two...
Normally, when Doctor Who slams two times together, one of them is the present. But the present travels with the show (almost) constantly in the form of the Doctor and companions, so every now and then someone (like Steven Moffat) writes an episode where two other eras collide. Aliens may or may not be involved - The Empty Child had the presumably-alien Chula offscreen, The Girl In The Fireplace had none. (Which on reflection makes it the first new Who episode entirely lacking in aliens apart from the obvious one, although not in monsters.)
Anyway, inspired by an LJ post by Trinity and Adventure! co-creator Bruce Baugh, an adventure hook...
Time And Treachery
from an idea by Bruce Baugh
The TARDIS lands with a worrying clang on a Thirty-third Century starship. As they explore, the companions are surprised by the wood panelling and brass fittings, but the Doctor shrugs it off.
“What’s wrong with having a nice bit of oak on your spaceship? Not like it doesn’t grow on trees...”
“But... hang on, is that a violin playing?”
Opening a double door, they look in on a large room and see a Regency ball in full swing. Gentlemen in Army scarlet and tailcoats, ladies in Empire line gowns, a band playing Mr. Beveridge's Maggot...
And all under a skylight showing the stars streaking past overhead.
The Doctor checks his watch.
Asking around, the dancers are suspicious but polite to strangers. They explain that they had been attending a similar event at Lord Weatherby’s manor, when an unearthly light overwhelmed them and they found themselves aboard “this strange vessel, whose portholes look out upon the stars in the heavens.” The crew put up no substantial resistance to the soldiers’ swords, explaining that they were historians, and apologising profusely for pulling them out of their own era and being currently unable to return them due to damage to their machinery.
This would be fine, a competent Time Lord can fix an experimental time drive in about half an hour... but the bravest of the Regency ladies and gentlemen have no desire to go home. As the ranking officer, a dashing Army captain, explains... “In the days since our abduction we have seen wonders undreamt of. Whole new worlds to explore, creatures out of myth and story living and breathing, the glow of a thousand suns. No doubt some of us would gladly return, and others miss family and friends, but you are explorers as well, surely you can understand the lure of another sky?”
Also, they may have optionally annoyed a Riven battle fleet. As you do.
Things To Do: Encourage the Regency adventurers to go home - their absence will have significant effects on history, from the missing captain changing the course of Trafalgar to those who would have children. Fix the time drive. And deal with the Riven boarding action while the captain and his men try to fend them off with cavalry sabres and the occasional duelling pistol.
Antagonists: The not-so-keen-to-leave Regency abductees, the Thirty-third Century, the Riven.
Action Scenes: Flying the spaceship through an armada, fending off spacesuited Riven pikemen, trying to fix the time drive, negotiating between future historians and Regency abductees.
Problems: Could be talky, with the aliens as a minor threat compared to the discourse on the ethics of time travel, the wonders of exploration, Regency society and the like. So it could be a fun change of pace, but the players should be in the mood for it. Equally, it could be run as more Master And Commander than Pride And Prejudice, although the clash of refined society with spaceships is part of the appeal.
Things To Prepare For: Throw in handsome gentlemen and charming ladies to stir up any romantic complications and jealousies amongst the travellers. Optionally map the pseudo-Napoleonic spaceship for when the Riven board it. Sketch in and possibly stat out the Riven, who I imagine as a typical bunch of irritable sorta-kinda-humanoids in funky spacesuits, but to further complicate matters could also be human. Figure out a quadrille.
Continuing the Adventure: An adventurous abductee who would not be missed by the timeline would make a great companion, the Riven could become a bother on different occasions (particularly if they get their hands on a time drive) and the Thirty-third Century historians are a likely source of further timeline trouble.