The UK (rightly) chose the current metric model, I.e. the MKS rationalised SI system. This is based on the metre, kilogram and second units, (also the Ampere, Kelvin and Candela for electrical current, temperature and luminous intensity) respectively. The whole system goes well beyond just length, weight etc., for instance, a litre is the volume of a 0.1m cube and that volume of pure water weighs1kg.*
Virtually every unit of measurement is defined in terms of the fundamental base SI units and most of them as as an integer power of 10. Where a measurement is much greater or less than the base unit, it is generally expressed in 10^3 steps,I.e. 1000 or 1/1000, hence mm, m & km. Some long-term metric using countries have been slow to adopt the standards which were set in 1960, e.g. Belgium still using cm.
* These equivalents are specified at certain temperature and atmospheric pressures as required.