The real question is not "will the Puma survive" but rather "should the Puma survive".
I would suggest Blackhawks would be a far better airframe for the mission than the Puma....less the one fact that the Puma is in the inventory and the purchase of the Blackhawk would cost money the UK Military just does not have.
After all...the Puma was "new" in the 1980's.
But then...with Blackhawks/Sea Hawks....the Lynx and Puma would both be indangered species. Perhaps Westland could do the same deal as they did with the Apache. Throw in some Kiowa's and you lot could be flying an all US Designed fleet less the Merlin.