250 knots below 10,000 feet is mandatory in all airspace classifications which rely on "see and avoid" to separate the traffic permitted to fly within them. That's ICAO class C, D, E, F & G. This speed limit is a mandatory requirement of the airspace and may not be relaxed by ATC.
ATC may relax restrictions in class A and B.
Unless the State allows otherwise.
In the UK, ATC may relax the restriction in Class D since it is a known traffic environment.
There is no restriction in Class C in the UK since it only exists above FL195.
The UK has no Class B.
There is no restriction in Class A in the UK, except where specifically mentioned in the AIP, e.g. on SIDs and STARs or within TMAs. So if you're flying along a Class A Airway below FL100 and there are no AIP restrictions, then you can fly above 250Kts if you wish.
Finally, the UK CAA will also issue dispensations for non compliance with the speed restrictions. Mostly these are for historical display or test aircraft.
Full chapter and verse for UK procedures can be found here:
UK AIC - Airspace Speed Limits