I don't have much to add to the discussion - it's a very odd encounter, and the discussion so far seems to be covering plenty of ground.
I do have a couple of observations, though.
The talk about 'Sandown Airport' perhaps makes it sound like it's a more extensive facility than it really is. It's a single runway grass field with a few facilities buildings in one corner. It serves very light (mostly single engine and micro/ultralight) general aviation traffic.
I stayed at the nearby Cheveton Copse Holiday Park last time i was down IOW way (in 2004, I gotta rectify that someday soon!), and there was barely any sound from the airport itself - the occasional engine drone from arriving/departing aircraft, but the only time I noticed the PA system was when crossing the field on the access road to/from the holiday park.
The holiday park is about 250m from the airport buildings, the area the encounter took place in is about 1km from them - sound from the airport would have to be noticeable in the wider area to account for the 'siren' sound being discussed. I'm not even sure the airport has one.
Whilst at 2km as the crow flies the quarry is 'nearby', it's more like 3km on foot following roads/paths, not a casual distance for a couple of small kids to cover in a short space of time. I think the quarry is probably a red herring.
The encounter is noted to have taken place in 1973, so I think the workmen must have been doing something unrelated to the downsizing.
From the same webpage, all IOW airports where closed during WWII, with their runways obstructed to prevent use.
Ventnor is not too far away, from an aerial perspective, and the radar station there was famously bombed at the onset of the battle of Britain in 1940, so its certainly possible other parts of the island had been as well, though I don't know of any incidents off the top of my head.
Oh. Now that gives me a 'wicked' thought!
Attached is an image cropped from the BBC test card image in use (and in colour) from 1967 and all through the 70's.
Green tunic. Unusual facial features, in unusual colours. A weird little hat, tufts of hair sticking out. Remind you of anyone?
Now, I'm not saying Bubbles the clown was the inspiration for a fanciful little yarn, but it was the first image to pop in to my head when
@WeirdExeter posted about colour television characters!
Also, apologies to
@WeirdExeter , I see all the quotes I've made are of your posts!
If I do manage to get down that way again soon (well, in the next couple of years!), I'll try and make time for a stroll through that wooded strip between golf course and airport!
Edit: For typo's.