Without Caller Id no signal will be sent down the line to give the callers number so there's nothing you can do at your end.
If you don't make many outgoing landline calls there are far cheaper ways to get a phone line - even allowing for the extra Plusnet charge for not having the phone with them. E.g. https://pulse8broadband.co.uk/line-packages
I wouldn't be so sure about that, I recently rang a company i had purchased goods from , my phone auto witholds caller ID , after several attempts and only getting their answer machine (did not leave a msg) to my surprise later that day they rang me back so they somehow got my number even though it is withheld, the emergency services can also see your caller ID
The telephone system, therefore, must always send that data, but CP's are able to block customers access to it, before Caller ID became common place, there was some equipment available that was able to retrieve the ID by itself