Thanks for all your responses. Although the question is as stated, to record the audio in both directions simultaneously, that does include Skype or any other VOIP activity, but preferably excludes OS System sounds.
Regarding audio recording quality, I only need sufficient bitrate for telephone speech quality. I had Freecorder 4 setup to record at 80Kb/s, but probably could be less than that, maybe 48 or 64Kb/s.
I gathered from Audacity’s home page its main purpose is more for musicians creating and editing high quality music, so immediately wondered if the suggestion to use Audacity to record in/out Windows audio was correct.
(btw, on a completely different topic, I am looking for articles that review Hi-Fi Active Speakers that can be used via a wireless (perhaps Bluetooth or WiFi) connection)
Although I prefer recording direct to MP3 for efficient file storage, I could live with recording to another format then delete after converting to MP3. I seem to remember in ancient days of 2,400 bps dial-up modems, my USR Sportster answerphone recorded messages in a proprietary format, but could be set to autoconvert to WAV.
As you say you formerly recommended Freecorder when in Version 3, in absence of a known standalone alternative, I wondered if I should seek that and try it out, so am grateful for the Freecorder 3 link to freedownloadsplace.com. I saw its a suitably small 2.2MB and downloaded it. I was surprised to receive a Windows notification ‘Open File - Security Warning - publisher could not be verified, sure you want to run this software: Freecorder Toolbar.exe.’. That is so rare, I can’t remember last time I saw that warning. Wonder why ? I cancelled the ‘install’ at that point as a) the Freecorder 4 toolbar that had disappeared after the FF autoupdate, has now re-appeared (although I have not yet tested it still works) and b) when thinking to install an App, usually I first check it is available and I can dl it without trouble, THEN I tend to read a little more about it before deciding to actually install it.
Am I correct in concluding Audacity cannot record a VOIP call in both directions ?
Even if it can’t, sounds useful for when I need to edit audio files. As it happens, I was looking for both a utility to extract audio from the various video formats including MP4 (see my 1 other post) and then save just a 2 minute part of resulting huge audio file, as a test file for evaluating Active Speaker quality. When googling for that, NCH software was top of the search result, and as it said there was a free version for private non-commercial use, looked no further, installed it, used very briefly once for 1 file, was impressed with it, unaware that next time I wanted to use it, it said ‘your 14 day evaluation has ended…’ !!! 
My preference is for open software, (really enjoy Inkscape) but for the various computing tasks I have, sometimes difficult to find a good open software offering, eg. a complete RDBMS with integrated Front-ends.