Standard weights and measures are maintained on behalf of the UK Government by the National Weights and Measures Laboratory (NWML) in Teddington; and it is against these standards that equipment manufacturers and Local Government Trading Standards Officers check weighing machines etc. There is a wealth of relevant information on the NWML website at http://www.nwml.gov.uk/nwml/role.asp
Possibly there are still standards kept in the Bank of England; but for practical purposes it is the NWML and Trading Standards Officers who maintain the various standards, and ensure that everybody adheres to them. Also, we have now gone metric, and whereas the Imperial pound could just be defined for the purposes of the UK, the kilogram is defined on an international basis. (Incidentally, I think there is a standard yard measure somewhere in Trafalgar Square.)
The original standard kilogram wieghts are stored in paris, geofbob and any country can check their standards against this. I used to work in a pertol station and can tell you from personal experience that these guys just turn up and do their thing. No appointments are ever made for these checks, although the post office are supposed to check their scales at the start of each working week.