I think the 'plip' is the key with the remote. There is a 'spare' key without a remote with most cars. It sounds like you don't have one.
However, if your key starts the car, it should work for the procedure. I think you just need a key with a valid immobiliser chip for security, so that the car knows it's OK to accept new remotes.
You would still need a new remote key, and you'd need to get it cloned at Timpsons. Again, an eBay key you can then give to Timpsons might save you a few quid. Mine came with no chip at all, so they cloned it from my other key and put it in the remote fob for £30.
If you are handy with a soldering iron, you could try an ebay repair kit:
https://www.ebay.co.uk/itm/174641545877 - this one comes with switches. You might find that you key is already paired and this fix could work.
@
ffrenchie You can get remotes at some Timpsons, different branches offer different levels of service. I had to travel a bit further to get to one that could do remotes. Their website explains who can do what and at which branch.