Whenever I have done that they have offered very little (or even the same) salary as I am on.

One time I was contacted about a role in London offering between 65k and 90k (can't remember exactly, but a range along those lines). I said I would only consider moving for the 90K end. He asked what I was on. I refused to tell him then eventually got wore down and told him my relatively small Spanish salary. He refused to put me through for that saying that it was not usual to get more than 10% more than what I am on.

The company was willing to pay more for "the right candidate", but my salary at the time meant I wasn't that candidate.

Don't disclose your salary to recruiters.

Anchoring effect. You're showing your hand in poker before placing bets. You'll never get a substantive increase in pay since the recruiter knows what you're currently willing to work for and that some small percent increase is still a win for you. Big jumps also usually means moving out of the range of jobs you're a "safe" fill for and that makes them view it as a higher risk of not getting paid for the effort trying to place you.

If you're not well networked and you're not enough of a rockstar to have companies approaching you out of the blue, your best bet is to control where that salary anchor is placed. There's hardly any way to verify your claim and you're almost always better off placing it at a believably higher position. I mean, companies aren't going to tell your their actual upper bounds for what they'll pay in salary, why should you tell them your actual lower bounds?