I've seen a job which appears a good fit but is 20% under my current salary. I wouldn't want to do it for that and the agent has said there is no room for negotiation. I don't want to waste everyone's time going for a job that I wouldn't accept at the advertised salary so do you think I should leave well alone or go for it and, if offered the job, negotiate?
If there's no room for negotiation, you are told that and then apply anyway and attempt to negotiate, you will not be successful and it won't go down well I wouldn't imagine.
Instead tell yourself that it's actually not a good fit, as a good fit would be at least around the same salary level.
It is always possible that you are one of those people who for one reason or another have ended up effectively being overpaid in terms of market rate for the job, and will therefore struggle to get something similar for the same money. That happens a fair bit, so if that might be a possibility I'd suggest having a think about how you market yourself as having extra skills and experience or consider the possibility that if you really want to move you may need to drop a little.