You should never have signed this at all. Their interpretation of it could be a claim for all your invoices if you wrote the vehicle off.
You gave them the right to take money directly from your invoice, so now all the hassle about sorting it out is yours not theirs.
They cannot charge you for damage to the barrier. They used the abbreviation i.e (“id est”= it is, or more commonly that is) that restricted their claims to vehicles. If they used e.g (“exempli gratia” = for example) the list would not have been exhaustive merely indicative.
They are allowed to charge for ‘the full cost of the repair’, not merely the parts.
If pursued I believe the matter could be resolved by reducing the total to £500, but the contract is practically useless on this point. The amount is dependant on 2 factors; cause and damage. Cause has already been specified in the contract and is limited to ‘your neglect’ (which would need to be established). Damage is undefined and does not even distinguish between the type of damage (e.g. they might charge you for bodywork but not punctures) or the amount of damage (e.g. small bumps are at cost of the repair and major crashes are handled by the insurance). Which party is to decide is also not specified, so arguably the decision is yours not theirs (though there may be a tacit agreement that by giving them ‘the right to make deductions’ you are also assigning them the right to make the decision). You should argue that the obvious inference was the claim would be the smaller of; ‘the full cost of the repair’ or the ‘insurance excess of £500’, otherwise the claim could be without limit (dependent on invoice).
But…
The company obtained an estimate for the repair which totalled £770 for parts (I was not being charged for the labour costs) and was told there would be a deduction from my pay to cover this.
Your post here suggests you knew the cost would exceed the £500 excess and you did not challenge the contract.
The company need to issue you with an itemised VAT invoice for the repair. For accounting purposes there is a difference between not earning the money and earning it and spending it on something (what you spend it on also matters).
Regardless of what else you do, I would contact your local council Trading Standards and try to get them to stop them issuing this contract in future. It’s pretty bogus, they should be invoicing you for any charges (which you could choose to dispute e.g. until negligence is established or the invoice amount is checked). Hopefully the next one will be written by a lawyer not an accountant.