You might find it hard to win a case before a civil court (seeking an order for payment to be made in respect of the writing of such letters if none was to be forthcoming otherwise) but, unlike Jackdaw33, I think that there's at least a chance that you might be able to do so.
The key word that you need to include within your letter is "offer". It has a particular legal status, which might be enough to swing things in your favour.
e.g:
"Sirs,
Take notice that I regard our correspondence with regard to the matter of xyz as at an end and that I will NOT reply to any further communications from your company other than as per my OFFER below:
OFFER:
I hereby OFFER to provide a response to any further communications you may send to me, in regard to the matter of xyz, for a fee of THIRTY POUNDS PER HOUR OR PART THEREOF for each such response sent by me and subject to the CONDITION that such payment is received by me within ONE CALENDAR MONTH of providing such a response.
TAKE NOTICE that the receipt by me of any further communications from your company, with regard to the matter of xyz, shall be deemed an ACCEPTANCE of the said OFFER.
Yours . . . "