We parked on the street, but there was a car park by the Danson House and Danson Stables (a pub). I believe it was free, as I couldn't find any signage with charging fees.
Large open fields and easy and flat walk.
There is a lake, or a boating pool. Of course, no boating activities were taking place, so it was very calm. Maple, of course, managed to jump into the water, but there were signs to keep an eye on your dog to avoid any incident with the wildlife.
Yes, there are poo bins throughout the park.
There is the Danson House, a beautiful Grade I listed Palladian villa that was officially re-opened by HM Queen Elizabeth II in July 2005 and opened to the public for the first time in thirty years. Also, there is a pub Danson Stables, built in the 1700s and originally a stable block, it's a Grade-II listed building surrounded by countryside.
Located in the London Borough of Bexley, Danson Park was an unexpected and pleasant surprise. The park is big, with vast open fields, a lake where you can hire a public boat, and a few other facilities like a café and toilets. The park was empty, not sure if it was because of the rain, and it was easy to navigate. There was only one negative aspect of the park, that I saw a few rats, as big as a chihuahua, coming out of the bushes near the water. But if you are in the southeast area of London, and looking for an alternative to the always busy Greenwich Park, Danson Park is a great destination.