It's usually more important to spend more on the lens than the camera. Personally, I'd try a used Sigma 150-600 Contemporary (about 650 GBP on amazon.co.uk) and a used d7100 (about 350 GBP for body only used). Maybe you could find those cheaper on another site. If you want to do birds, a 600mm on a crop sensor is the way to go (or a very expensive FX that you can crop a lot). I like the Tamron 150-600 g2 better, but it won't fit in your price range.
You can also find the Sigma or Tamron 100-400 for maybe 500 GBP used. That would be the fallback and get you into a kit for maybe 850 (with amazon.co.uk prices). A 400mm on a DX would be 600mm equivalent, which is passable for birds.
You can also do a refurbished or used Canon 7d (mark i, not the new one) for about 325 with any of the above lenses in Canon format. But personally, I'd take the d7100 over the 7d, as I shot with the d7100 for a while and it was a good camera. I've not used the 7d, but wanted to throw out the Canon route too. Camera bodies come and go and you can keep upgrading them. The glass usually lasts a while, so if you invest in good glass you can keep rotating bodies through it as they become affordable to you. Remember, the cost of a body is what you paid minus what you sell it for.
For the d7100 you can add an 18-55 AF-P for about 85 GBP used. it's a great walk-around lens. Make sure it works on the d7100, I'm pretty sure it's compatible. I'm sure Canon has a similar one for a 7d for about the same price.
You might also be able to get a Sony RX10 mk iii (20-600 equivalent, 14 fps) for 900 some. It's a little out of budget, but might be a better all-around camera and lens than the above options which are only on the long side.
Marc
P.S. the link you shared didn't work for me, so I don't know what you linked to