A few links to the relevant law and guidance on it:
Wording of defence of lawful excuse under the Criminal Damage Act -
https://www.legislation.gov.uk/ukpga/1971/48/section/5
CPS guidelines -
https://www.cps.gov.uk/legal-guidance/criminal-damage
More general defences, in particular defence of necessity -
https://assets.publishing.service.gov.u ... L42-v1.pdf
The third link refers to preventing phyical injury in the context of necessity, so it is not clear to me whether it would or would not apply to preventing interference with property. If it did, it seems that the test would be whether the damage was proportionate to the interference caused/harm done.
The CPS guidelines contain the following example:
A motorist who damages a wheel clamp to free their car, having parked on another's property knowing of the risk of being clamped, does not have a lawful excuse under the Act: see Lloyd v DPP [1992] 1 All ER 982; R v Mitchell [2004] R.T.R. 14 CA.
That suggests to me that there has been no similar example, ruling or test case for a situation where a car was clamped *without* lawful authority to do so and the car owner destroyed the clamp to free their car.
I am not a lawyer, but it appears to me based on the above that someone may be considered to have a lawful excuse if they destroy a bike lock to free their own bike. Moreover, I doubt that the CPS would want to pursue a prosecution in such a case, because they would probably decide that it was not in the public interest* and possibly that there was less than a 50% chance of a successful prosecution.
* Public interest in this case being that the under-resourced CPS and criminal justice system have got far more important things to do than waste their time clarifying this aspect of the law in a trivial case caused by an inconsiderate selfish jerk who deserved to have their lock destroyed (and their bike stolen if that was the consequence of their bike then being left unocked). However, even if that might be the eventual decision of the CPS, one would run the risk that the police would arrest someone destroying a lock.
If it were me, and especially if my bike was expensive, after waiting for what I considered a reasonable period for the other bike owner to return I would probably destroy the lock if I had the means to do so. Before doing so however, I would call the police using the non-emergency number to report what had happened and ask for their assistance. The police would be very unlikely to attend/help, but I think it would help your case if you could show that you had done everything reasonable before destroying the lock.