Well, I do actually have the very same Nick Kamen boxers from that Levis 501 Laundry advert.
https://www.sunspel.com/products/me...in-white-mbox4700?_pos=1&_fid=4b63dbd9b&_ss=c
They was supplied to him from a company still trading today, called Sunspel, and not only that, they are based in my home town of Long Eaton, Derbyshire, UK
Just be warned Sunspel is not cheap (Think the ones Nick had, normally go for £30+), but if you are able to get to Long Eaton like I can, they do have a factory shop, typically selling stuff at a 3rd of the normal price.
Also if you happen to go into Harrods for their own branded stuff, it's Sunspel that supplies those.
https://www.sunspel.com/collections/mens-underwear