The answer to this question was already found, this is just so that
Bobbie7-ga is able to post it.
Thank you

Hello again Neoba,

From the Royal Mail Website:

?Managing your address data correctly can make the difference between
keeping and losing a customer.  The Solutions Directory is a
comprehensive listing of independent companies who provide products or
services based on the Royal Mail Postcode Address File (PAF), National
Change of Address File (NCOA), Universal Suppression Service (USS) and
Business Changes File (BCF).?


The Solutions Directory 
Either search by the service you need, or enter more specific detail.
http://www.royalmail.com/portal/rm/solutionsdirectory?catId=400084&mediaId=12400135&pageId=dir_landing&redirect=true

I selected ?Data Cleaning and Verification?,  pressed SUBMIT and
obtained 12 results

Licensed Resellers 1-7
http://www.royalmail.com/portal/rm/solutionsdirectory?catId=400084&mediaId=12500162&pageId=dir_search_results&_requestid=163852

Licensed Resellers 7-12
http://www.royalmail.com/portal/rm/solutionsdirectory?pageId=dir_search_results&currentPage=2&catId=400084&mediaId=12500162


Search terms:
Address Verification software UK Royal Mail


I hope this is helpful!

Best regards, 
Bobbie7

That's what I needed
(I don't know how I could miss it when I searched myself, but that
doesn't matter, so thanks Bobbie7!)
that was not a very hard one in itself, but I appreciated your
reactivity since the question was posted

Thank you for the tip!
--Bobbie7