As a period piece, this is perhaps beyond criticism. The soundtrack is fascinating to any lover of 60s psychedelia, with Pink Floyd foregrounded (almost every track from A Saucerful of Secrets is sampled at some point), as well as the Moody Blues, Cream and so on. And the lover of London's history gets to see the locations in its 'swinging' period.
But, as a Londoner of the time would say, it ain't half dull. Had the brainwashing techniques of the Ipcress File been adopted by the London Tourist Board, the result wouldn't be too unlike The Tyrant King. Long montages of the three children exploring the Imperial War Museum, or Hampton Court, or St Paul's, are interspersed with dialogue to the effect of how impossible it would be to find the villains in a city the size of London, followed immediately afterwards with the three children bumping into one of them, and then running away. Which makes you wonder why they were looking for them in the first place.
The anorexic plot doesn't help - there is virtually no motivation for the children at all, they just bumble through a series of incredible coincidences, starting with the initial overhearing of a telephone call in an unoccupied house, in which they have no business, at the very moment that someone decided to use its phone. Incredible that this classy production team could create something so spectacularly tedious.