It is my fault I didn't get this sorted. All I can say is:
* The contract had been extended many times, always with the same terms.
* In the past, when I had sent the agency a copy to countersign, it often seemed to be more faff than it ought to have been.
* I saw the signed copy sent by the client to the agency & guess I figured, well, we've all agreed to this, this is fine.
* There was a lot else going on & we were discussing possible terms of future work, which didn't pan out, so my attention was mostly on that.
Sorry if I was less than clear in the opening post viz. not insisting on getting [the contract] countersigned - obvs I am not feeling great about this - however it turns out, it will be a lesson learned.
The fundamentals are: The client will pay the agency for the work & we have an agreement evidenced by emails, even if there is no physical signature on the document between me and the agency.
How strong a position would I be in assuming, worst case scenario, that the agency didn't want to pay?
I just want to know what I should do now and move on.