Scratch a great actor and you often find a born comic underneath and, watching Ian McKellen’s itinerant solo show, I was more than once reminded of Ken Dodd.

McKellen shares the late comic’s total devotion to theatre so, to mark his 80th year, is touring that number of venues across the country. And, like Dodd, McKellen treats the audience not as passive spectators but as one half of a double-act in an evening that becomes a form of acted autobiography.

McKellen could hardly ignore Gandalf, and the show begins with a reading from The Lord of the Rings and an invitation to a young lad from the audience to wield the wizard’s sword. But McKellen’s heart and soul is in theatre and the first half of the show is an exploration of how the love affair began. We get stories of McKellen’s early excursions to Peter Pan, Ivor Novello musicals (he claims that it was at King’s Rhapsody “I had my first erection”) and pantomime. This last leads McKellen to dip into the theatrical skip behind him, don a headscarf and instantly turn into a gossipy Widow Twankey, hurling sweets into the stalls before asking: “Anyone like a banana?” We hear naturally of McKellen’s coming out and the burden that lifted from his shoulders.

While that’s a now familiar story, I was struck by how it relates to the whole saga of the McKellen family. It is fascinating to learn that so many of his forebears were lay preachers and so many of his relations teachers. There is clearly in McKellen an inherited campaigning zeal, whether it takes the form of pursuing gay rights, championing live theatre or preserving the idea of companies. While he laments the passing of the permanent rep ensemble, he also demonstrates its shortcomings: evoking the 80-year-old butler he once played in Agatha Christie’s Black Coffee, he lapses into a form of quivering antiquity hilariously at odds with his own octogenarian vitality.

If the evening is a series of love letters to theatre, it is Shakespeare who gets the most mail. In the second half, McKellen asks us to shout out the names of all Shakespeare’s plays and, as we do so, he gives us an anecdote, a reminiscence or an extract relating to each one. He is at his best, and his simplest, in the “seven ages of man” speech: at one point, his voice even pipes and whistles in a way that signifies old age. But McKellen also proves the value of Irene Worth’s comment that “when you’re doing Shakespeare, you should jazz” and offers a series of riffs on everyone from Romeo to Macbeth. It is an extraordinary feat, and rather like watching a music-hall memory man with an obsession for the Bard.

I’d like to have heard more about McKellen’s mentors and even about directors who have helped shape his career. But you can’t have everything and, in just over two and a half hours, McKellen takes us on an engrossing voyage round himself and the British theatre and, wherever he goes, donates the takings to a cause specified by the venue. At heart McKellen is a missionary with the technique of a vaudevillian.

• Touring until 15 September.