I hate cleaning those carpets, they always look patchy after cleaning but dry out evenly. Clearly as said you have over wet in an effort to get rid of those carpet knee kicker filtration marks. Sounds like they have got the bug for a new carpet and expect you to pay for it/them.
Hopefully you've got 'item being work upon' cover, and not just 'public liability'. Even so your excess will probably be £500.. which you will have to pay per claim.
They, however are not entitled to a new carpet, as insurance cover is on an indemnity basis - what the carpet was worth before you touched it. Fortunately you took before photos, they can give the insurance company a better idea on working out settlement and by the looks of it, they weren't worth much.
If it comes to it after attempting to rectify, If it was my I'd offer them £400.. towards new ones. That way you'de probably save £100.. on your excess and avoid your next premium being hiked.
Dave.