I've just tried to buy something on eBay and a little window keeps popping up which sais ..........privacy-keep.com

Firefox has prevented this site from asking you to install software,

I've been using eBay for years and have never seen this before.

What should I do about this.

Could be malware embedded in the listing maybe?

Just did a search on name and it looks like bad news. You need to clean it up, maybe something like malwarebytes would help. If you're lucky just your FF installation may be hosed, otherwise it could be system's connection stuff. NEVER install anything unless you know what it is and are certain of it's source, especially when it's forced on you -- you did right to back off. Keep away from ebay and anything involving personal info until you get passed this.

In the meantime might be a good idea to download chrome or some other browser from portableapps.com

These portablesapps versions install everything inside the installation directory you choose (even if it's on a thumb drive), and doesn't affect the rest of your system. When you want to remove it you simply delete the directory tree, no need to run any sort of uninstaller.

I was in a public internet place once, downloaded the portableapps version of Firefox and when I tried to use it I got a pop-up that said "Use IE, you idiot"

Using a portable apps version of Chrome will more than likely NOT afford any more protection over the normally installed version. In fact, since the files are probably hosted some where in your home directory, they can easily (without UAC prompts) be overwritten with no escalation of privileges required. Stuff in Program Files at least is protected from being overwritten by UAC since you need admin privileges to make changes.

O.k so I gather it's a virus.

I only have Windows defender on my computer.

I've sta a scan with that but it looks like it will tke an hour or two.

If that doesn't work I will MallwareBytes.

I have a copy of my O.S on a hard drive but it has been plugged into the computer till now

Looks like Firefox caught and prevented it installing. Still a good idea to download and run Malwarebytes, there's loads of stuff like spyware and adware it can detect that a virus scan wouldn't be concerned about.

I did a Windows defender scan and it found ne threats.

I downloaded MalwareBytes and did a scan and it detected 193 threats.

It seems to have worked because there is no trouble on eBay anymore.

Is there something I can do to stop this happening again.

You could purchase a better security package (I use Kaspersky Internet Security for example). I also believe the pro version of Malwarebytes offers real time scanning as well, you could have a look at that or just run a scan as often as you feel the need manually.