I highly doubt that OP's ds would have a problem with getting into Eton when he is already able to get into at WUS.
Also based on that, I doubt he is unable to get into the Westminster senior school either.
Westminster has great facilities, and depending on what your DC wants to do, there is a lot to do.
They bought a separate building specifically to improve their sports etc. they have a proper professional music studio, even shooting gallery.
Central London schools are moving the fields monopoly away from boarding school nowadays, as most of them actually buy parts of playing fields and gardens around Central London.
Nor does Eton have a monopoly on guest speakers or resources.
The following statement does not apply if your dc got into WinColl, Westminster, St Pauls:
a) Eton has become too meritocratic and competitive for their son(s)
b) They failed to get a place having gone through the process
c) They cannot afford the fees any longer.
My DC went to different schools as they have different personalities, and DS2 did not want Eton.
OP I was hung up on the concept of boarding school outside London, but I am seriously considering London base for my younger DC. You can't go wrong with Westminster. As a thoroughly London person, I love it here, and it's rubbed off on my DC and they see their future here.
Logistically, it would may be better for you to attend to your DS as you are used to doing things at WUS anyway. Your ds has the day option if things don't work out. If he is happy at WUS, just keep him there, his social life won't have that much of a change (visits to local friends, you as a family just around the corner - I presume)