Plumbing – What type of connection is this to the spigot

It's called a tap connector (obvious now I've found it), and you should be able to unscrew it. You can see one here

It's the bottom nut you need to be turning. It's part of a joint that attaches the pipe to the tap.

Once you have this off you should be able to remove the tap as normal.

If it's stuck then something like WD40 or penetrating oil might help. Failing that carefully heating the nut with a heat gun might expand the various parts enough to loosen them. Take precautions to avoid getting direct heat onto the bath (it appears to be acrylic).

A more drastic approach would be to take a hacksaw to the thread to separate it that way.

This is what worked for me (it's rather brute force, but functional):

• Take a small C-clamp (I had a 3" one laying around) and place it in the mouth of the spigot on the right hand side with the body of the clamp facing down.

• Tighten the clamp

• Twist the clamp counter clockwise using the body of the clamp as a gripping surface and leverage

• If it doesn't work try tapping the spigot with a hammer or mallet to jar it loose a bit then try the clamp again.

Note: this may damage the spigot a bit, it was useful to me as the spigot was already broken and all I had available was a hammer and a clamp.