I've just watched the video by Jayz, and it seems the first of two variants of 4060 Ti (8GB version) will be available at $399 (so probably £399-ish here) is launching next week. The 16GB variant, which will apparently be from partners ONLY, will be $100 more and not until July.
Fortunately, and in contrast to the great 4080 debacle, the ONLY difference between 8GB and 16GB versions is the amount of VRAM. No cutting corners elsewhere as per 4080.
Anyway, as the basic 8GB version is (according to Jayz) the same price as the 2060 Super and 3060 Ti were, this might well appeal to those wanting 40xx, but at a more budget-friendly price point.
Jayz video is here