This looks like Amazon's version of Just Eat etc where you order from certain restaurants and they deliver it to you. As with Prime Now, it is limited to some London postcodes to begin with but will surely rollout to most places.
1. Download the Amazon or Prime Now App
2. Order from Amazon Restaurants
3. Enjoy you meal
£10 off your first order over £15, use code AMAZON10
HUNGRY10 might work for existing customers.