Inspiron 5567 Combo Audio Jack

I get a pop up screen when I plug something in asking if it is say mic OR headphones

There is no option to select "headset"?

In addition to the popup, open the Windows Sound dialog, on the recording tab, and make sure that "microphone" is enabled and selected as the default device.

I have an external splitter lead which claims to handle both mic AND headphones.

The splitter is supposed to work that way, but very often the mic part of them won't work. It could be because laptop audio ports sense the presence of a microphone by its impedance, and the adapter could be interfering with that process.

Way round is a USB audio device.

A usb interface or audio jack would be a good workaround, because then you eliminate bothl the problem with the Realtek/Waves popup, and the problem of using an adapter with the combo jack.

For me the reason this is crucial is at my church. My old laptop had 2 jacks In and Out. We could say play a backing track which goes OUT to a mixer desk and then comes back In with vocals added for recording. Any other ideas?

That setup in combination with a combo jack is less than ideal. Even if you get the microphone function of the combo jack to work, it is still just a mic jack and would produce a mono recording. On your old laptop, the audio input jack might have doubled as a mic jack and a line-in jack. Most of the Dell laptops used to have that feature. Modern laptops no longer have the hardware to do what once was commonplace.

I suggest getting an external  audio interface that has a stereo line-in jack. Line-in would be more appropriate for accepting the line level signal from the mixer, than a mic jack which is meant to receive a much lower signal.