Colour Wow Supernatural Dreamcoat. £24 a bottle from Amazon. If you Google around you might find a sample size to try for about £12 online.
I have hair as pouffy and bushy as yours, trust me this stuff is gold! And I've tried every smoothing, de-frizzing and flattening product available over the years, including morrocan oil.
Dreamcoat essentially coats your hair with silicone, and you have to use heat to seal it (and flatten the cuticle) - so you spray it on towel dried hair, without any other products at all, and then blow dry with a brush (you don't need to be an expert in blow drying straight, you're just pulling some weight though the lengths and angling the nozzle straight down the hair shaft - I do it fairly cack-handed and it still works).
It may still look pouffy when dry, but it should feel lovely and silky - run the GHDs through it, boom, smooth and glossy! The downsides are that it does build up on your hair, so only use it every other wash and invest in a good clarifying shampoo to clear it every 3rd week or so and start over - otherwise it starts feeling sticky and dull. I use Toni & Guy Detoxifying shampoo.
If you've got £200 to spare, you could always have a salon keratin treatment (see pic of my hair, that was my before and after) - but it's high maintenance and only lasts 2-3 months. That's why I just use Dreamcoat now, it's way cheaper with just a little more effort required!