There is a "rule" - as MancBoy sums up, from the UK AIP...
Minimum Rates of Climb and Descent
2.2.1 In order to ensure that controllers can accurately predict flight profiles to maintain standard vertical separation between aircraft, pilots of aircraft commencing a climb or descent in accordance with an ATC Clearance should inform the controller if they anticipate that their rate of climb or descent during the level change will be less than 500 ft per minute, or if at any time during such a climb or descent their vertical speed is, in fact, less than 500 ft per minute.
2.2.2 This requirement applies to both the en-route phase of flight and to terminal holding above Transition Altitude.
Note: This is not a prohibition on the use of rates of climb or descent of less than 500 ft per minute where necessary to comply with other operating requirements.