This covers all of the UK and is a great way to search all the places by county. Some larger National Trust gardens are listed and also smaller privately owned gardens such as Gotha Gardens at Pembroke Farm where our pictures were taken for our last photoshoot.
In my county of Hertfordshire, Benington Lordship garden near Stevenage is on my list to visit and has a number of dates coming up on which the gardens are open and you can pre-book.
Cornwall has some beautiful gardens listed if you get a chance to go. Some of the ones that I have visited include the Lost Gardens of Heligan, Trelissick Gardens near Truro and St. Michaels Mount gardens (both National Trust), and also Tresco Abbey Gardens on the Isles of Scilly.