Why do they need a performance document? Just because you've had issues at one job with management does not necessarily mean you'll have the same issues, or any issues, in the new one.
As others have said, many employers these days will only confirm dates you worked from, dates you worked to, any sick days/absences and if you're the subject of any disciplinary proceedings if asked (in, for instance, healthcare, teaching etc). If they give information about you that is false or unsubstantiated, they're laying themselves wide open to challenge, tribunals etc. You should definitely be able to ask for a copy of whatever they say about you.
Mostly when I've left jobs I've left on very good terms but there have been a couple of instances where if they had asked my previous line manager for a reference they would have told them I was an insubordinate mare. (The fact that those particular previous line managers were mickey-taking workload-piling-on inefficient narcissists who couldn't run a tap if it didn't have a shiny award attached to it would not have been apparent.) Sometimes when I was a line manager if we had references given that seemed questionable we would then go to the 3rd reference, and often it was obvious from that that the line manager's reference was just a serious personality clash between a couple of individuals.
"Criminal behaviour, industrial espionage, sexual harassment" would usually come under gross misconduct so be quite apparent under "reason for dismissal", surely? And if it was serious criminal behaviour, then that's what the DBS/CRB checks are for.
I think I'd be inclined to ring HR at your old job and explain the situation, confirm with them that they can provide a reference stating dates, etc, and then get in touch with your new employer explaining that the policy of your most recent employer is to only provide factual information; or, if you can, get the old HR dept to do that. (Sorry, that sounds more convoluted than it should.
If you find yourself in a position a friend of mine did, where her company had the utterly dopey policy that HR wouldn't give factual references and you had to approach the line manager (another situation where the line manager was not renowned for her amazing people skills and ability to get the best out of staff, to put it mildly; this particular line manager also had a policy of only giving references AFTER staff had left, making it very interesting, since many companies won't offer you a job without satisfactory references. My friend ended up having to get 4 references, I think it was, from all her previous managers over the years, all of which were glowing, so that the new employer could see the pattern. Abusive, toxic employer with lousy record-keeping and mini-Hitler manager? No, absolutely not....) then that's a bit more of an issue.