"TDC" does indeed stand for Tristan da Cunha, the tiny volcanic island in the South Atlantic Ocean in whose name this "coin" was produced. In commemoration of the 500th anniversary of the accession of Henry VIII.
Your coin is not gold. The denomination is "five pounds", not "half sovereign"; the half-sovereign coin will be quite small. Your link helped confirm, however, that these were made by the "London Mint Office", a private mint with a pseudo-official-sounding name and a less-than-sterling reputation. You would have had to pay £120 for one of these
new off the LMO website, but it's only sterling silver, with a thin gold-plate and a couple of gimmicky gemstones; the secondary market is virtually nonexistent. Your coins also appear to be damaged, unless that's a trick of the lighting. I'd value it in the £20-£50 range?
If you don't get any takers at that price, you can go to Tristan da Cunha and maybe get a fiver for it.

Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis