Online Instrument DealersMost specialist brass shops have websites and will sell by mail order. Here are a selection of links to the second hand pages of some of these dealers:
The Wind Section
Trevada Music (trumpets)
Trevada Music (cornets)
Once Loved Musical Items
Gerry Birch Music Services
Non-Specialist Second Hand DealersCash Converters
EbayHere are links to searches restricted to results from the UK:
Classified Ad SitesGumtree, will return national listings so you will need to narrow it down to your area.
cornets for sale on Gumtree
trumpets for sale on Gumtree
Physical AuctionsYou need to pay buyers premium and they won't usually post items, you need to be able to collect. There are a few online bidding services used by auction houses. Here are some of them.