Having found and met my cousin, thanks everyone for your good wishes.
I made a large book of photos and ancestry to take with me to give... The agency was brilliant setting up a nice room and being there with us when we first met (and follow up with counselling afterwards if needed). I am glad I didn't give up searching, and my elderly cousin thanked me for finding... They had always wondered about their birth family. The birth mother died when I was a small child and the 'secret' of their baby was told to me as a teenager. I always felt it was an injustice that this unknown cousin was denied the opportunity of contact, if they wished for it... But an elderly relative of the birth family was against contact. So I took up my quest after they passed away, and I'm glad I did. I hope this helps others in similar situations.