Hi Fantree,
There are two taxes in question here.
Capital Gains tax on the disposal of personal assets and income tax on profits of items bought and sold with the intention of makinga profit.
The trading income allowance is only available to set against profits for income tax, where your are self employed as a sole trader.
It cannot be set against capital gains arising from the disposal of personal assets.
If you dispose of a single asset or a collection of items, for more than £6000, you are required to declare it.
Have a look at:
Report and pay your Capital Gains Tax.
Thank you.