If, during the SID, ATC say, ‘climb FL XX’, you need to reply, ‘confirm climb now or climb via SID FLXX?’, and act on the result. This has happened to me a few times recently, and the result has been, ‘sorry, I meant climb now FL XX’.
If you reach the end of the SID, at 6,000 ft (unheard of), you should maintain 6,000 ft, and attempt to contact ATC. If you aren’t able to contact, adopt radio failure procedures. I’ll need to look at the precise wording again, for the possible case that the lateral track causes you to leave CAS as the base steps up away from London; there might be an argument that once outside, you need to stay outside (but knowing you’ve gone outside might be tricky). Practically, ATC would expect you to climb back in.
This whole climb now/via SID is just stupidity. Our aircraft are like hammers being used to drive a screw in; the rules are totally unfit for purpose.