The Obligatory Disclaimer: Unfortunately, I don't own Doctor Who or any associated characters, creatures, features, gadgets, gizmos or TARDISes.
Wilf had sensed that the Doctor was upset about something when he returned to the little kitchen and - with proper English hospitality, the Doctor remarked - had immediately poured two cups of tea. Now they sat in the library through the door, facing each other across a small, round, wooden coffee table. Wilf was reminded uncomfortably of that conversation they had had in the tiny café in London - only two days ago? It seemed like a distant memory now.
"So if we're going to be stuck here for four and a half hours," said Wilf, breaking the uncomfortable silence that hung in the air, "don't suppose I could use a...you got a phone, or something? Sylvia and Donna - they'll have heard about the nuclear explosion by now. They'll be beside themselves."
"The nuclear explosion is still happening," said the Doctor. "It will be until the TARDIS is running. I said we weren't moving anywhere in time or space - we are at a fixed point on the timeline of this exact physical location. Our own timeline inside the TARDIS is no longer relative to the exterior."
"So if I were to walk out that front door..." Wilf began hesitantly.
"...you'd be vaporized," the Doctor finished. He was looking over Wilf's shoulder with distant eyes, scanning the towering shelves of the library thoughtfully without seeming to see anything inside the room. Wilf waited, and eventually, the Doctor blinked and returned his attention to Wilf.
"You can explore a bit if you like," he said, with forced cheerfulness. "There's an exact replica of the Hanging Gardens of Babylon behind the cinema. Or have a look around in here - or is it the library behind that shelf - Gutenberg himself printed me a copy of the Munich Manual of Demonic Magic. The TARDIS can telepathically translate any foreign language inside your head..." He trailed off - Wilf was watching him seriously, trying to catch his eye. The Doctor avoided eye contact and sipped at his cup of tea.
"Where is he?" asked Wilf.
"Safe." The Doctor swallowed hard, blinked several times, and Wilf felt almost painfully awkward, brought repeatedly back to that café. In the number of times he had encountered the Doctor, he had never seen him as he had been over these past few days... Wilf couldn't imagine what the Doctor had been through, what he was still going through. What must it be like, he wondered, to witness your entire race, your entire home planet, just annihilated, as if they had never existed...and then to have them reappear, lingering for a few heartbreaking minutes, but to be forced to banish them with your own hands. Except for one... No wonder he was risking everything to save the Master, Wilf realized.
"Look, I might be just an old man - well, a child next to you - but if there's anything I can do..."
"I shouldn't have got you involved," said the Doctor bitterly.
"Well, you were hardly going to leave me behind, were you?" Wilf pointed out. "And you couldn't have gotten out with him without me. No, I think I got myself into this - my old mum always did say I had a knack of running into trouble." He chuckled as another thought occurred to him. "And did you hear my Sylvia hollering blue murder when we left? She knows me as well as my old mum did - and she knows you too! My word - me and you - quite a pair we make, eh?" The Doctor couldn't help but smile at this.
"So, Donna and Shaun?" he said lightly. "How did they meet?" Wilf was glad of the change of subject, and happily poured two more cups of tea while he filled the Doctor in on the comfortably everyday lives of his family. At one point, he could have sworn he felt something brush past his feet, but when he reached under his chair to swat at it, he found only dust and cobwebs.
Eventually, the tea and conversation ran out, and the Doctor announced he had to check on the TARDIS repair process.
"You stay here," he said, standing up. "I don't want to have to come and find you if you get lost in the corridors of the TARDIS! Just stick to these rooms." Wilf stood up more slowly – he was beginning to feel that morning's mad dash to the TARDIS in every joint.
Stacking the teacups after the Doctor had left, Wilf eyed the kitchen door curiously, and for a moment, he thought he felt something prick the back of his neck.
"Not bloody likely," he muttered with a grin, depositing the teacups on the table and heading for the door. Just a quick look around wouldn't do any harm…
...
An alarming "clunk" came from somewhere beneath the console room, and the Doctor jumped. He gave a round black button on the panel a last frustrated jab, and leaned back against the railing, taking the weight off his injured foot. They had crept forward a fraction of a second, but essentially, they were still stranded. Gallifreyan symbols ticked slowly across a screen, calculating the repair rate of the defensive shielding, but as the Doctor's eyes expertly followed it, the whole screen blanked out and turned a startling shade of blue, Gallifreyan symbols replaced with meaningless white characters. Angrily, he slammed his fist down on the panel.
"No no no!" he growled in frustration. "Not now – please, not now, not-" He stopped short, drew a breath and ran his fingers almost apologetically across the console. "Sorry, old girl," he muttered. "You didn't ask for this either." With a weary sigh, he pushed himself upright, seeming only more weighed down by the slump in his shoulders, and turned to head back down the TARDIS corridors.