From the recent thread on get_iplayer 3.05 no longer working due to changes at the BBC's end and 3.06 not working for me either on CentOS 7, a bit of digging later I found I now needed to have the perl-LWP-* packages installed, which weren't previously required. I did have one of the perl-LWP family present, previously that was enough. Now, after installing the rest of perl-LWP (and all its dependencies) all is working fine.

Hopefully this may help others running into the same problem.

Presumably you didn't have the LWP::Protocol::https module installed. That has been a listed requirement for get_iplayer for some time. Unfortunately, not every distro will install the HTTPS support along with the rest of LWP. With the BBC intent on HTTPS everywhere, you can't do without it now.