My knowledge of Spitfires & TR6's is not much past knowing what parts don't fit on my car.
The TR6 engine is a stroked version of the GT6 engine (thanks to I think Andy Mace for pointing out the development order).
So there are similarities. As far as headers go, Kas Kastner in his GT6 Competition Preparation Handbook pointed out that fitting a header as opposed to using the stock cast iron exhaust manifold gained power in the upper end, but cost power in the lower end.
And not just a little. Notice that the header doesn't equal the stock manifold's power until 4,000 rpm. For a track car, this is not a big problem, but it is for a street car (which Kastner points out in the "Building a hot street GT6" section). Just as a daily driver, you'd have to keep the revs up over 4,000 to justify the header. Pulling away from stop lights would be sedate.
For a street GT6, the stock cast iron manifold makes more sense. It may be the same for a TR6.
A new design of header for 6 cyl Triumph engines has lately been available called the "Phoenix" extractor. Instead of the typical 6-2-1 design, it is a 6-3-1 design. A lot of folks have claimed it to be an improvement over the typical desigs & not only less detrimental at lower revs, but superior to the stock manifold. I've never seen a dyno graph comparison, though, so who knows. You can claim anything, & the "butt dyno" is hardly reliable. The variations being sold of the 6-3-1 headers are interesting: they can vary among other things in the length of the primaries, which in general header theory is where low rpm power is controlled. So with all these 6-3-1 manifolds being sold in various configurations - they're not all the same. Anyone who'll drop $600 on one, dyno it with a standard header & the stock manifold, & publish it would get my gratitude.
Kastner probably published a TR6 Competition Preparation Manual for British Leyland; you might watch eBay for one. Kastner sells on his website a compilation of some of the material he wrote for BL: <u>Spitfire, GT-6, TR-3, TR-4, TR-250, TR-6 Triumph Preparation Handbook</u>
https://www.kaskastner.com/kasbooks.html
Which will likely have very useful information for you.