Another Parent Page issue

Hi all

I have noticed that the option for selecting a Parent Page is not showing my editor – either on the live host or on my local computer.

So, I did a fresh install of Wp5.2.4 using TwentyNineteen and create a simple page, and the Parent option appears! Clearly, something is amiss on my production site!

More reading… I came across a post on here that suggested checking the JSON response using http://dev.bedsastro.org.uk/wp-json/wp/v2/pages – which I did, and got a hold load of data back – which I assume is good! The start of the data looks iike:
[{"id":5027,"date":"2019-10-29T11:19:22","date_gmt":"2019-10-29T11:19:22","guid":{"rendered":"http:\/\/dev.bedsastro.org.uk\/?page_id=5027"}

So, next I go back into my site, log in, go to a page and the Inspect and I can see a number of errors in the Console.

One error is this:
Failed to load resource: the server responded with a status of 500 (Internal Server Error) which has a link of http://dev.bedsastro.org.uk/wp-json/wp/v2/pages?per_page=100&exclude=4112&parent_exclude=4112&orderby=menu_order&order=asc&context=edit&_locale=user

Another has the error:
Uncaught (in promise) Response with a link of data.min.js:1
Inside this error, there is:

body: (...)
bodyUsed: false
headers: Headers {}
ok: false
redirected: false
status: 500
statusText: "Internal Server Error"
type: "basic"
url: "http://dev.bedsastro.org.uk/wp-json/wp/v2/pages?per_page=100&exclude=4112&parent_exclude=4112&orderby=menu_order&order=asc&context=edit&_locale=user"
__proto__: Response
arrayBuffer: ƒ arrayBuffer()
blob: ƒ blob()
body: (...)
bodyUsed: (...)
clone: ƒ clone()
formData: ƒ formData()
headers: (...)
json: ƒ json()
ok: (...)
redirected: (...)
status: (...)
statusText: (...)
text: ƒ text()
type: (...)
url: (...)
constructor: ƒ Response()
Symbol(Symbol.toStringTag): "Response"
get body: ƒ body()
get bodyUsed: ƒ bodyUsed()
get headers: ƒ headers()
get ok: ƒ ok()
get redirected: ƒ redirected()
get status: ƒ status()
get statusText: ƒ statusText()
get type: ƒ type()
get url: ƒ url()
__proto__: Object

So, the (hopefully obvious) question is how to diagnose what is causing the issue?
I guess an initial step is to disable all plug-ins and see what happens…
I could also enable one at a time, but I guess there is the possibility that a combination of plugins are causing the issue…

Is there a way to track down the root cause?

Thanks
Darren