You consider it unlikely that they know of the damage. However you asked for replacement paper, and your line manager may have asked if damage is covered or something. Either way this form has arrived. Whether by chance timing or connected, we don't know.
I would not accept that form. Its a classic thing in employment, don't accept extra obligations without some form of compensation (pay, etc).
It's also a classic of negotiation/discussion to state your own position, rather than just weakly defending against/objecting to theirs.
Hence, instead, I'd reply something like this:
Regarding your email and form, I am confused by these.
Of course, like all of us, any employee is responsible for deliberate damage done to company property. That's normal and expected, and should be in any contract of employment anyway.
However your form is suggesting something completely different. At face value, it's suggesting that all employees are liable for all costs to any damaged equipment - whether accidental or otherwise. Also in addition, that this should be retrospective from today back to whenever they first joined the company, and that thus may be claimed when they leave.
I don't think that is the intent behind it, but that's actually what the wording implies, and therefore with regret I cannot sign it. It literally leaves too many doors open and is too open ended and vague.
By way of example, if a chair breaks, or a tool fails, during use, or a person accidentally pulls a cable out and breaks it, will there be a bill on their final day of work for all such matters? Including all those from first starting until today? I cannot imagine that is the intent. But it is the actual wording.
Standard UK law is that employees are not responsible for run of the mill accidents, loss, or damage, provided they did not do them deliberately. I look forward to confirmation that this is actually what is intended by your email.
Best regards, ...
If they argue, maybe add this observation (in your own words) to any reply:
It also gives leeway for anyone who wanted, to charge pretty much any amount to anyone, after any amount of time passed - after all, who broke a cable years ago? Who else had used that chair and perhaps weakened it? Should the "damage" include just the cable, or the full cost of a service call and lost time of a department? There is massive potential open-ended liability, enough to potentially bankrupt any employee.
You may get pushback.
Companies tend to want forms signed and contracts changed when they want it. But in this case, it's too big to do that.
Even if they agree to a list of past damage they propose to charge, or confirm there isn't any known, they could "discover" some later, or blame you tomorrow for something with a 4 figure bill.
You can't sign this, or anything like it. You dare not. Even if it costs your job. So there is no point in discussing it or negotiating it, as if you could sign it. You have to state your position and that's that.