BtVS by Whedon and Mutant Enemy. Doctor Who by Davies and the BBC. Some inspiration drawn from IDW's published StarTrek/DoctorWho comics.
Scripts from BuffyWorld dot com used as reference. In this case, Season Five's Triangle.
In the alley outside the Magic Box, Sunnydale's one-stop spot for spells meant to brighten life on an active Hellmouth - at least, that was the use for most of the items the proprietors actively tried to keep in stock - a deep whirring sound could be heard, the sound of cosmic gears clicking into place.
In slow pulses, a blue telephone box emerged into reality, settling itself down onto the concrete. A man of average height, with short brown hair, burst from the doors in a burst of frantic activity. Taking a few moments to reign himself in, he cricked his neck, rolled his shoulders and took a few deep breaths. Despite the relaxation of the rest of his body, the toes of one of his feet kept up a steady tap-tap against the ground.
"Bloody Hell," a voice said from behind him. He whirled around to take in the leather-jacketed appearance of Spike.
The blonde vampire had been lounging on some crates, taking advantage of the deep shade and indirect sunlight to enjoy a cigarette break. "That's one way to arrive in style," Spike said. "Although I'm not sure what kind of style you're going for."
"Unforgettable." The man bowed. "Anything else is pointless."
"Wot?" Spike's lip curled. "Are you actually British or are you making fun of me?"
"I'm from the North," he said with a grin. "Most planets have one, although when you're dealing with donuts it can get tricky. You can call me the Doctor. You must be William the Bloody."
"Great," Spike snarled. "Another alien. We slaughtered the last one. You here on your own reconnaissance or did Glory get a wholesale discount? If I'd known it was easy to get things from outer space I wouldn't have bothered with the Order of Taraka, stupid waste of money that was. My reputation from the Scourge spread to other planets already?"
"No, just your future poetry. Most of it's the same as your old work, you just needed encouragement from a better audience."
"Ah." Spike glanced from side to side, then stuck out his hand, making sure to keep it in the shade. "Nice to meet a man with good taste."
The Doctor shook the offered limb happily, then brushed past Spike to enter the store.
Anya frowned as the vampire and the alien emerged from the back stacks. "What have I told you about bringing in friends through the back door? I get suspicious and I have to waste time redoing the inventory and it takes time away from my boyfriend because the one time we tried to combine the two he got this awful bruise on his-"
Willow coughed loudly and started speaking before Anya could continue. "I'm sure any friend of Spike's is a non-enemy of ours - he likes us. I'm Willow and this is Anya."
The Doctor smiled politely and walked between the ladies towards the counter. His all-purpose sonic screwdriver, set to silent mode, as he'd been afraid it might be mistaken for a weapon, vibrated faster in his pocket as he neared a suitable target.
He began rummaging around the stacked objects with one hand, while the other dove deep into his pocket to come out with a pair of spectacles that had a jeweler's scope attached. Placing them on his head he grabbed a crystal off the counter and spun around to face the others, one eye freakishly enlarged.
"Brilliant!" He held the purple crystal dramatically up to the light. "A compartmentalized crystalline matrix using Maddox style encoding. I haven't seen one this fine in a century."
"While I appreciate your enthusiasm," Anya said, forcing a smile to her face. "That particular item isn't for sale. It's from the owner's personal collection and I'm not allowed to sell his stuff while he's on vacation. If you could, please return it to where it was serving an aesthetic purpose. Might I offer you a great deal on freeze-dried toad auras?"
Willow blinked, a memory falling into place. "That's right, that's the crystal Giles recovered last month." She turned a stern eye on Anya. "I don't think it's supposed to be on display either. We don't have the spells to use it properly, so it's too dangerous to activate."
The Doctor scratched his chin. "Nope, seems straightforward enough. Just a simple push on the right tangent of reality will execute its self-contained unfolding instructions. No chance of us switching places with its contents, unless you happen to be a force of chaos or just that unlucky." He pulled out his sonic screwdriver and, after restoring the sound effects, spun through the settings. "If it's a matter of not knowing what's inside, I can pull that up right... now."
Willow froze as the Doctor aimed his screwdriver at the crystal in his hand. Anya grabbed a sword from behind the counter and held it ready.
A small holographic image of a horned man, dressed in furs, appeared on the counter.
Anya blanched. "Right. I know him. He wasn't purple and see-through last time I saw him, but I'd recognize that hammer anywhere. He's Olaf, he's a troll and that hammer has some divine buffs. He was a renowned fighter until he dropped off the face of the Earth. Good to know where he ended up."
The Doctor grinned. "Divine buffs you say?"
"Yes. He's been blessed by the Troll Gods. Quite the hero if you're a troll. Ironic considering he made quite a reputation killing them before I turned him into one. It felt like appropriate justice when he cheated on me back when I was human. Um." Anya froze and started back-pedaling. "Not that I'm not human now, or have ever been anything else. We also don't sell anything as dark as that here, not unless you can wait a week and are willing to pay for the premium order-"
Willow face-palmed. "Anya!"
"Well, now that you know what it is, could I buy it off of you? Not the troll, he's a living being, but I'm quite willing to cover the price of the hammer. Now," he waved, his hand at the Magic Box's main table, where a copy of the Sunnydale Press lay folded. "If you open that, you'll find yesterday's winning lotto numbers and a matching ticket."
Willow laughed. "Matter creation's impressive, but all that stuff is registered by computers. A simple forgery just isn't going to cut it."
"Now, Willow," Anya nudged the young witch. "Let's not be too hasty. I've lived through enough rewrites of reality to at least want to check out his story. If there's enough time magics going on, he could've known this was coming... And there's always the chance that he won the ticket naturally and is being stupidly theatric."
She calmly walked over, grabbed the paper, found the ticket in it and walked back to the phone, while Willow pulled out her computer. A short call to the gas station the ticket had apparently been purchased at and a confirming nod from Willow soon had Anya scribbling out an official receipt. "Sold," Anya said, as she thrust the piece of paper at the Doctor and ran out the door, stopping only to flip the sign from 'Open' to 'Closed.'
The Doctor opened the doors to the TARDIS and stepped inside, closing them very firmly behind him. He leaned his back against the doors and closed his eyes, as if to put all the evils of the world behind him. A short 'ahem' had him opening his eyes, to see Rose tapping one of her feet impatiently.
"Would you mind," she asked. "Telling me why you insisted on me waiting in here?"
He shook his head, reflecting on the short conversation he'd had with Willow and the few dollars he'd managed to borrow from Spike. "Ever heard of Buffy the Vampire Slayer?"
"The show from the States? What... You mean we're in that Sunnydale? You can hop into fictions too? Or is it some sort of amusement park planet, like the one for Sherlock Holmes?"
"Nope, not my doing. I doubt that much exists out there, besides the main bulk of Los Angeles, but I'm not about to check. Rupert Giles might be creating an overlap with his Britain right now, though, and that frankly scares me. There's something out there trying to put false memories in my head, to make the connections real and I'm not about to let that happen."
"Count me in." Rose nodded. "I'm not about to let my ma be in danger from vampires... Well, any more than she is already. What can we do about it?"
"Same thing we always do," he said, holding up the purchased crystal. "Throw a spanner in the works and see what happens. I know enough about this scenario to take things completely off the rails and, with this, I'm two-thirds of the way there."
He walked over to the TARDIS controls. "Rose, make note of the time. If we don't go much further into the future than this, we might get everything wrapped up before anyone else dies. Right now, let's head into the past and into Los Angeles proper. The next thing for my plan's there, somewhere, but I frankly have no idea what I'm going to do for the last one on the list."
"Really," asked Rose as the engines started up. "What is it?"
"... An evacuation plan."