You can put up a sign, but that doesn't change the law. It's like when people put up "Your car will be towed if you park here" signs where they'd _like_ you not to park, doesn't change my right to park there (does increase my chances of doing so though, because they couldn't just ask politely).
If you’re asked to leave you have to but trespass itself is not a crime, it’s purely a civil matter.
See the opening sentence from the CPS website:
https://www.cps.gov.uk/legal-guidance/trespass-and-nuisance-...
E.g. you have the right to “rest” on land adjacent to the side of a footpath or bridalway. Now the definition of “rest” is undefined because that’s how common law works.
So you can probably make the argument resting includes camping over night (when leaving no trace) until someone proves in court that it doesn’t.
Here’s another fun fact: you can also legally ride a bike on a “footpath” so long as you discount when you come to pedestrians. That one was clarified in Hansard but people blindly assume that they don’t have that right without checking.
The point is, things are usually legal unless there’s a law and legal precedent to say otherwise.
Really asking: Wouldn't a "no trespassing" sign be considered an ask to leave?