From the UK AIP ENR 3.2.2.3
Maximum Rates of Climb and Descent
In order to ensure the credible interaction of Airborne Collision Avoidance Systems and ground based safety nets, other than aircraft in emergency and certain specific conditions for military aircraft (as detailed in Military AIP and MAA Regulatory Publication RA 3000 Series), all aircraft when operating under normal circumstances, when inside Controlled Airspace within the London and Scottish FIRs/UIRs should not operate with a climb or descent rate exceeding 8000 ft per minute. Aircraft when first approaching a cleared flight level and/or when changing flight level in Controlled Airspace should ensure that the vertical closure speed is not excessive. It is considered that, with about 1500 ft to go to a cleared level, vertical speed should be reduced to a maximum of 1500 ft per minute and ideally to between 1000 ft per minute and 500 ft per minute. Pilots should ensure that the aircraft neither undershoots nor overshoots the cleared level by more than 150 ft, manually overriding if necessary.
Minimum Rates of Climb and Descent
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.
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.