The last consultation for fully privatizing ATC wasn't even responded to by AOPA or PPL/IR, which suggests most pilots just don't care.
I think you're confusing how NATS is owned with how ATC in the UK is funded. The consultation was about the former, not the latter. NATS recovered its costs and more from users long before it was privatised. The effect of privatisation from the users' point of view was probably an efficiency improvement, and thus lower costs.