Six Delta
If you are flying from one of the London TMA Airports and the radar controller tells you to climb to a level above your SID level then you can climb to that level unrestricted. In fact, I will rephrase that, not 'you can' but 'you should'.
That is how we operate in the London TMA. I would suspect that other TMAs in the UK are the same.
For example we will sometimes will give a/c that are on a restricted SID a higher level in an effort to beat Heathrow traffic because we know that the Heathrow traffic will be stuck down at SID levels due to stacks etc.
It would be potentially dangerous if that a/c was then to follow the SID climb profile before dawdling up to the higher level.
The SIDS in the TMA are designed around Heathrow and are done to provide initial separation only - if we can give you a higher level we will do - our aim is to get you up and off our frequency as quickly as is safely possible. No controller in the TMA should give you what is effectively a conditional climb to a higher level (the condition being follow the SID levels)
Unless you are given a condition to any clearance, then you should fly your a/c in accordance with the clearance as soon as you are in the correct configuration to do it.