How switch Mac UK PC keyboard layout backslash \ and backtick ` to match normal UK PC layout

It appears to be controlled by what you actually have connected... but there is something else going on I'm still trying to hone down.
The best conclusion I can come to at the moment is "it's a bug" but one that seems to be at least partially fixed in High Sierra & Mojave.

This is a UK Apple Keyboard on Mojave [confirmed identical on High Sierrs]

When you first open the panel, it shows as ANSI.

Press Shift [which I discovered by accident trying to take screenshots] & it changes to ISO.

Then add British PC & it seems to retain that information...

Now I've persuaded it to show like that I can't 'break' it again, it seems to stick so far.

However, testing on El Capitan, I can't persuade it to flip to ISO, no matter what I do - it stays as ANSI...

Test on the El Cap machine, swapping a TextEdit document from British to British PC - even though the control panel still claims it's ANSI & after clearing all keyboard prefs & re-detecting the keyboard...

The Mac 'knows' it's ISO, but won't display as that in the Keyboard Input Sources control panel.

Make sure you have configured the Keyboard settings under Keyboard > Change Keyboard Type... first.

Once you have configured the Mac in ISO mode the right settings should be applied, you may need to remove and add the input device (British -PC) afterwards.

You need to run the Keyboard Setup Assistant again, and the only reliable way to do that is to delete the files it generated as follows (run this in the terminal):

sudo rm /Library/Preferences/com.apple.keyboard.plist
rm ~/Library/Preferences/com.apple.keyboard.plist

Then restart your computer. When you log in / plug in the keyboard it should show you the Keyboard Setup Assistant and ask you to press the key to the right of the left shift, i.e. the \ key on a normal UK keyboard. Do as it asks, and it should detect your keyboard as ISO (not ANSI). Accept that, and then make sure in System Preferences -> Keyboard -> Input Sources you are using the British - PC layout.

That should give you a normal keyboard layout, with one exception - the Ctrl key (the bottom left one) will be mapped to the Mac Control key, which you rarely use, and the Windows key will be mapped to Command. You probably want to swap those so that copy/paste shortcuts etc. are the same as on Windows.

The easiest way to do that is to install Karabiner-Elements and set it up like this:

Also note that this keyboard layout is not applied before you log in after a reboot, but it is applied before you log in after logging out. Very confusing if you have " or @ in your password!

You seem to have a US (ANSI) keyboard, where there is no letter key to the left of the Z. Is that correct? For a "normal" UK layout, you must have a European (ISO) keyboard which has this extra key.

If you do have an ISO keyboard with extra key, then you have a keyboard type problem.