There are still paths into iPlayer that do not need an account. Check out WebPVR (https://github.com/get-iplayer/get_iplayer/wiki/webpvr), or if you’re feeling brave, the command line tool that underlies it, get_iplayer. It was originally written as an iPlayer client for Linux users, but has been backported to Windows as it has many advantages over the official interface.
You almost certainly do need a UK IP address, but no account registration is needed. It downloads programmes as a simple unencrypted MPEG file (complete with metadata) that you can play in your favourite media player (e.g. VLC), keep indefinitely, transcode to other formats etc.
Since this tool is a reverse engineering job on the iPlayer protocols, it does break from time to time, but the authors usually catch up. I have successfully used it to download the programmes we’re discussing in this thread. Doubtless the BBC will be working hard to close the loophole, but enjoy it while it lasts.