That website says they are out of stock
These are not Z rated tires so why max speed rating shown is 168 MPH, yes I know you would not go that speed
but that does say the design is lessor then a Z rated which rate at 186 MPH
As shown, they are Summer only tires
They really used here in the USA for like drag racing, they are soft and not have much of a tire life
It's always worth speaking to North Hants; it does get regular deliveries and the staff know what's coming in. However, it wouldn't surprise me if there were significant delays due to the logistics issues at the moment. The last time I ordered Nittos from them, I had to wait eight weeks (and took an alternate course at that point, anyway).
With regards to the rest, I know â but, in the UK, I'm personally not aware of any other off-the-shelf (effectively) choices. So, well, if you want new tyres...
You do occasionally see the older Toyo Proxes R888 listed but I doubt stock even exists for these, and that's an even more aggressive option.
Most, as you suggest, aren't going to attempt such speeds â or even drive their cars that hard â anyway, and most are just fair-weather cars. I'd always swing for a mainstream high-performance tyre myself, with appropriate ratings, but if such a thing isn't available...
Even Longstone Tyres, a vintage and obscure tyre specialist in the UK, doesn't have anything in 315/35 R17.

Remembered it this morning and had a quick gander.