The box came first. The Metropolitan Police put police boxes up across London between 1928 and 1937, and the design that became the best known was drawn in 1929 by the Met's own surveyor and architect, Gilbert Mackenzie Trench. Around 1,000 of his boxes were installed between 1929 and 1938, and in 1953 there were still 685 on the streets of Greater London. Personal radios made them redundant, and they were phased out in the late 1960s and early 1970s.
Doctor Who first went out on BBC television on 23 November 1963, when the boxes were still an everyday sight. The TARDIS — Time And Relative Dimension in Space — has a chameleon circuit meant to disguise it wherever it lands, but the Doctor's always looks like a 1960s London police box, and inside it is far larger than out. At the centre of its console room is a hexagonal console with a moving column at its heart, the time rotor. The shape now belongs more to the show than to the police: the Patent Office accepted it as a BBC trade mark in 1996, the Metropolitan Police argued that it should be theirs, and in October 2002 the Met lost its appeal and was ordered to pay £850 plus costs.
The figure standing by the console in this kit, grey-haired in a dark coat, looks like Peter Capaldi's Twelfth Doctor, who arrived in "The Time of the Doctor" at Christmas 2013 and regenerated in "Twice Upon a Time" at Christmas 2017. The series made him a capable guitarist, and there is a guitar in the room. His console room was the one that added bookshelves and a second staircase up to the gallery, and the kit follows it: staircases on both sides, galleries of bookshelves above, an armchair and a small table with a teacup below the console, and a ceiling hung with rings of clock-like gauges.
ETKVR is the house brand of Dongguan Sile Crafts, a craft-kit factory founded in 2019 with a production base of more than 5,000 square metres in Dongguan, China, that also makes kits for other sellers; the same CH08 is sold as ASLOWSNAIL's Mysterious Telephone Booth. The kit never says Doctor Who — Amazon's listing calls it inspired by the blue police box of the 1950s and 1960s. Sile Crafts lists it as 256 components in UV-printed, laser-cut wood, with a battery box and wires, an instruction manual, paper accessories and a dust cover, building to 18 × 13 × 23.5 cm. The doors swing on real metal hinges, and a clear PVC tube etched with a pattern spreads the blue LED light up the time rotor; it takes two AAA batteries, not included, and is rated 14 and up. Shops give other figures for the same kit — HiNooki says 368 pieces, eight to ten hours and intermediate, with a touch switch on top to turn the lights on.