What cabin would you want to travel in? Do you intend to make a cash booking and use Avios to reduce the price? Or make a reward booking with Avios (plus taxes/fees/charges)?

If the latter, Avios prices for reward bookings don’t fluctuate in the same way cash fares do. For London-NYC it’s 50K Avios in Club World off-peak, 60K peak, plus TFC. There’s also a reward saver price of 62.K with lower surcharges. This article has a useful table: https://thepointsguy.com/guide/ultimate-ba-avios-guide/

So, when there’s best value from a reward booking is when cash fares are at their highest. Though the main aim of the game with Avios is finding availability. Luckily NYC is one of the easier routes to get Avios availability on.