Amex is offering 2,500 Membership Rewards points (worth 2,500 Avios amongst other things) if you spend £250 on flights, hotels (pre-paid) or car hire before 1st August.
The Amex travel home page is here – you should see the ad for this promotion on this page.
I am not sure if booking hotels via Amex Travel counts as a third-party booking or not and therefore takes away your chance of earning hotel points, stay credit and elite benefits. It probably doesn’t, since Amex is not a rooms wholesaler like Expedia. However, you may want to be careful here.
The best thing to book is probably a flight, since it will have no impact on the miles you will earn.
This is effectively a 10% rebate if you value Avios points at 1p and spend close to £250, so it is worth seeing if you can find a way to use it.