What you have been told by eBay there is not correct.
Ebay are required to report your sales to HMRC if you sell 30 or more items or earn more than 2,000 euros (approximately £1,700) a year (Jan to Dec). However, provided you are only selling unwanted personal possessions and not buying/making items to sell then you will not need to pay any tax or inform HMRC.
The £1,000 quoted is the trading allowance for business sellers and does not apply to private sellers.
£6,000 is the threshold for Capital Gains Tax, so doesn't apply unless you sell an individual item/collection for £6,000 or more.
https://www.ebay.co.uk/help/account/regulatory/sales-reporting/uk-digital-sales-reporting?id=5454