New on the BA website today, some destinations are now on sale in July and August in WT according to BA's sale banner.
A cursory look suggests some savings of £100-£150 on the previous peak fares (although I didn't record the peak fares - its just too hard to capture everything!).
You are not going to get to NYC for £400 but it is cheaper than last week and as it is school holidays and the Olympics probably as good as you'll get for this peak period unless BA have over-estimated demand and need to sell seats off nearer the time.