eBay/Amazon may work on a volume/value threshold as to what they consider a business seller but as far as HMRC care as long as you're not buying to sell -- are clearing out unwanted personal items -- you're a private seller.
Selling lots of duplicate items, if applicable, may raise suspicion.
That's a separate question from tax,
https://www.gov.uk/capital-gains-tax-pe ... ossessions
But with two of you spreading that activity and bearing in mind that bulk dealers such as MusicMagpie mean that popular titles generally aren't worth a great deal, it'd have to be a giant collection for that to come into the equation.
Not a lawyer or accountant, but I play one for purpose of auditing.