What GOV.UK says
Anything posted or couriered from another country goes through customs. Depending on the goods and shipment, VAT, Customs Duty or Excise Duty may be payable.
Who handles the border process
The parcel or courier company takes the goods through customs and normally tells the recipient when an amount is due. Keep tracking and shipment records so you can respond to a genuine notice.
Your responsibility
Make sure the sender declares the goods correctly and check whether the goods are banned or restricted. Incorrect information can lead to seizure, penalties or prosecution.
Why there is no threshold table here
Rates, thresholds and processes can change. A copied number quickly becomes misleading, so this page links to the maintained GOV.UK source instead.