Just in time for Halloween, the new Doctor Who’s ickiest adventure yet skitters onto the screen. Alongside the horrific punning, "Arachnids in the UK" is a rip-roaring bug hunt sure to induce a cold sweat in anyone with a creepy crawly phobia. It also features Mr Big from Sex and the City (Chris Noth) doing a comedic Donald Trump impersonation opposite Sunita from Coronation Street (Shobna Gulati) – which can only be a good thing.

But for all the thrills and chills the episode, written by new showrunner Chris Chibnall, is the most problematic example yet of the issues starting to bedevil the 13th Doctor. It’s obviously fantastic the BBC has moved with the times and given us a female Timelord – but four instalments in, is it too much to hope the hyperventilating wide-eyedness that defined the character early on might have matured into something calmer and less flippantly cartoonish?

Again this week, Jodie Whittaker’s Doctor conducts herself like an eight-year-old hopped up on fizzy drinks trapped in a grown woman’s body. When, for instance, sidekick Yasmin’s mother – Gulati – wonders whether her daughter and the Doctor are an item, Yasmin (Mandip Gill) pulls a face. But the Doctor behaves as if she doesn’t quite understand. “I don’t think so…” she muses. “Are we?” Please – give us a Doctor who does understand. With each passing hour she more closely resembles Tom Hanks in Big.

There are other problems. The army of outsized spiders on the loose in Sheffield is impressively rendered – how far we’ve come from the era of the Sellotape and bin-liner Doctor Who monster. But Chibnall overreaches trying to make us empathise with the “big bad” arachnid which has crawled from the toxic landfill beneath the swizzy new hotel built by hard-charging mogul and presidential wannabe Jack Robertson (Noth).

Good-hearted Gallifreyan that she is, the Doctor is trying to lead the creature, grown too huge to breathe and slowly suffocating, to safety when gun-toting Robertson – sigh… Americans, Chibnall all but exclaims – walks in and shoots it dead. This is supposed to be a moment of pathos – Free Willy with eight legs and crushing mandibles. But a giant sad spider is still a spider. That howling silence is the sound of nobody’s heartstrings being tugged.

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Where "Arachnids in the UK" succeeds is in again making Yorkshire – the squad are finally back after the Tardis has decided to behave itself – a compelling sci-fi backdrop. And the dynamic between the Doctor and her team of Yasmin, Graham and Ryan has gelled into real chemistry. They truly feel like a gang on an intergalactic lark. There is also some humour in the use of Stormzy and his arachnid-friendly beats to lure the spiders into a trap.

Whether there is a romantic spark between Yasmin and the Doctor (she is wearing rainbow after all) or Yasmin and Ryan (Tosin Cole) is, on the other hand, a question left for us to ponder. But it makes perfect sense for Graham (Bradley Walsh) to proclaim that, with his wife Grace dead, there is nothing tying him to his old life and we share the crew’s excitement as they clasp the Tardis’s gear-stick together and whoosh off to their next adventure. Wherever they materialise Whovians will hope Chibnall is less sentimental about the monsters. Carry on like this and by the end of the season it will be hug-a-Dalek week on Doctor Who.