Last bit first:
No, you can't counter sue. (What for? You'd need to have some reason to make a claim against her).
Send her a letter by recorded delivery. (Yes, I know that she lives downstairs and that you could drop it through her letterbox, but you need proof of posting, and of receipt). Retain the receipt from the post office and (via a screen grab) take a copy of her signature upon receipt from the Royal Mail website.
Your letter should be dated and show both your name and address and that of your neighbour. The wording should be roughly as follows:
"Dear Mrs Bloggs
In response to your claim for compensation for damage to your property in respect of a water leak which occurred within my property, I hereby make the following offer WITHOUT PREJUDICE:
(i) I will arrange to have all water-soiled clothing professionally laundered or dry-cleaned (as appropriate to the materials) at my expense or, alternatively, I will reimburse you for any payments which you have made, or may make, in respect of such laundering or dry-cleaning arranged by yourself, subject to the provision of valid receipts for such payments ;
(ii) I will arrange for the professional cleaning of any water-soiled carpets within your property at my expense or, alternatively, I will reimburse you for any payment which you have made, or may make, in respect of such cleaning arranged by yourself, subject to the provision of a valid receipt for such cleaning.
TAKE NOTICE that no further claims in respect of damage to your property will be entertained by me unless proof of such damage is provided by you.
Yours sincerely,
Michael James"
It's absolutely essential that you keep a copy of that letter, together with proof of posting and of delivery. Then, if your neighbour is foolish enough to take you to court, you can show that you have acted entirely reasonably.
UK law normally only allows someone who has suffered damage to their property to receive appropriate compensation for such damage. Occasionally a court might consider a claim for 'distress' or for 'exemplary damages' (e.g. if you'd held a party involving everyone spraying each other from hosepipes, with complete disregard to your neighbour's property) but, in general, nobody should expect to profit from a compensation claim.
Incidentally, if your own insurance offers 'third party' cover, you should speak to your insurers before making any formal contact with your neighbour.
Chris