Prices will be similar to the RTX 3060 (at least £490), which it presumably will match in performance. Nvidia is way ahead of AMD in terms of selling GPUs (and production output), so they can still set the prices of the market.
I think prices could improve, if Nvidia decides it's worth releasing desktop versions of the RTX 3050 and 3050 TI.
What's odd about the whole situation is, it has been about a year since the Ampere series was released, usually the whole lineup would've been released by now (excluding 'Super' versions ofc).
Edit - The price of the RX 6600 XT is currently around £460-470, so I'd expect the RX 6600 to retail for ~£50 less.
It will be interesting to see how much the RX 6600 can be overclocked, it has a TDP of just 150w.