Hi, I just joined this forum so I could confirm that Classic Parts Shack is still trading, to help others who may see this thread (the only review of Classic Parts Shack I could find online). As Vista pointed out, they are are not a registered company, but operate as a sole trader or partnership, I would guess run by an older couple.
I ordered an NOS part for my VW Scirocco in the early hours of Sunday morning, choosing their cheapest delivery option - Royal Mail Signed for 2nd Class. Email and text message confirmation came straight away, followed by despatch notification later on Sunday, complete with Royal Mail reference number (not trackable before delivery). The part arrived well packed and in good condition on Wednesday.
Hopefully this post will reassure anyone who has come across Classic Parts Shack and is looking for reassurance about its continued legitimacy.