Thanks for that confirmation soundman.
I'm a bit more awake now, but it still perplexes me.
How can a LED prevent power on?
And if the load current was too high for the switch, it wouldn't power up without the LED.
AHA - there we have it - the 20mA LED is enough to overload the 10A switch and hence.... (No - I won't say "now way", but that is essentially ridiculous; a switch instantaneously failing with an additional 0.2% (over)load.. no way!)
And yes, Archy tried the other switches. So we have ruled out the switches (unless it's a weird batch fault!) and the connection topology, and connections.
I'm gonna love the solution to this one - especially if it's another one of my Do'hs! that is so obvious. (See if I re-quote my last reply's first line - damned woosy oldfart!)