Had the same trouble for Aug 2017 & having same trouble for 2019! We like the Yacht & Beach club. All rooms were available until the week before 'free dining' was announced! Then they only had a turret room on club level for the Yacht Club at £20,000 + for the room (excl flights). Only club level rooms were available at the Beach Club. I phoned Disney, who tried to tell me that it's a popular time for UK visitors! A few weeks later standard rooms at the Beach Club became available so we quickly booked with an agent. They advised that if any better rooms become available, we can alter booking!
I think they remove a lot of rooms from the UK free dining deal. More and more people chose to visit & I think some room types are kept for the US market.
Try phoning a uk agent and ask them to give you a quote with a US company. It may be slightly more expensive but you can still get free Disney Dining. They won't be able to give the $200 gift card.
We could have booked this way for the Yacht Club, which we may have done had the Beach Club not have become available!
2 years ago we had the same problem! We ended up booking for the Beach Club but had a problem with the room and was offered a room at the Yacht Club! Funny as we had booked direct with Disney who told us throughout the year that no rooms were available there!!!