The wait is over. After a bit of a hiatus and two Christmas specials, proper weekly Doctor Who is back and the fact that episode one of series ten is called The Pilot is not to be taken lightly. There’s a reference to a pilot within the script, but you could – if you’ve just materialised from a parallel, Who-free universe – take this as your jumping-on point.

Touted as a pilot episode, it explores afresh the key concepts and joys of this 54-year-old show through the eyes of newcomer Bill Potts. She asks all the right questions that any normal person would – and then some. It may take Bill some time to work out that the Tardis is bigger on the inside – but thanks to her we finally discover the exact location of the Tardis toilet.

To backtrack, though, the Doctor is established as a lecturer at university, apparently somewhere in Bristol. He’s been based here a very long time (decades) and gives enthralling lectures on Time and Life. He has his own gorgeous wood-panelled, red-painted quarters adorned with a Rembrandt self-portrait and etchings on the walls and his police box sitting in the corner. For die-hards, this will smack of Shada, the unfinished and unaired 1979/80 serial written by Douglas Adams, which had Tom Baker’s Doctor visiting a Time Lord professor at Cambridge.

More, it reads like Educating Rita, only without the booze, as Peter Capaldi’s prof decides to become a private tutor to Bill, a canteen worker who has an enquiring mind and slips into some of his lectures. Capaldi is even more magnetic than usual and, importantly, Pearl Mackie is instantly winning as Bill. The fledgling companion is a 20-something who lives with her foster mother, works at the university and develops a crush on a young woman she’s been serving generous portions of chips.

The Pilot focuses on building the new friendship between the Time Lord and Bill, yet there’s plenty of room for Matt Lucas returning as the Doctor’s batman, Nardole. Lucas has impeccable comic timing, spinning sarky asides, peculiar squeals and amusing lines, at one point quoting Kenneth Williams from Carry On Spying.

If you were expecting a complete reboot for Who next year under new showrunner Chris Chibnall, well it almost feels like Steven Moffat has accomplished it a year earlier. There are fleeting nods to the past (the Doctor has portraits of two “family” members on his study desk), otherwise this episode offers a fresh take on an old format, given an energetic snap from young director Lawrence Gough.

I’m not going to say much more for now but some points to watch out for… Beware the menacing puddle. Hold on for the Daleks and an old foe of theirs. And whatever you do, keep alert until the very last second. Jaws will drop!

Doctor Who returns to BBC1 on Saturday 15th April