You could try a few different locations in the UK. They don’t usually get all of them.

Mozilla uses Mullvad under the hood so no surprise if both doesn't work if one doesn't.

Anyways, you light have to change your locale and/or time zone. I've used iPlayer successfully with Nordvpn myself for a while now.

Might need a dedicated IP for that. I had some success in the past with the Proton VPN premium/streaming option, not sure what the exact name is

I have been using a linux vm setup on azure as vpn for years and it works great for iplayer.