If I have many objects on the page and I give each one an id field name is there any way to export them all at once each to a separate png file with the id field as filename.

I can do it with the export dialog but only one at a time by selecting 'selection' then 'export'.

Or is there some sort of script etc. or extension that can do this?

Ok I found a script to do it.
https://github.com/berteh/svg-objects-export

Seems to work well so far

And this doesn't work?

Yes that works, I installed the plugin then noticed the batch export there and thought it was added with the plugin but if it's the default setup yeah it works great

Yes, it's there by default