Many thanks to all you for your helpful posts. I think I've stressed myself quite a lot.
However, I had a discussion with new ClientCo and told them the whole situation. Manager said, he is happy to send me an email stating that they want me to work for them and they don't want to involve any agency. This will clearly show that Agency didn't lose business and in fact it's the Client who doesn't want to involve any agency. Actually they are thinking to get rid of that Agency.
Client is also happy to write in the email that that the relationship is not of type "Client". It's partnership relation for few of the products. Hope this will make my case stronger.