The links below are to gardens I have personally visited but do not have any good pictures to include. I would recommend these gardens to anybody interested in gardening as they all have varied selections of plants and are beautifully landscaped. Most are in the north west of England which has a great variety of wonderful gardens to visit.
Arley Hall & Gardens (Northwich)
These gardens are very good in summer with a famous double herbaceous border.
Wonderful walled garden which I think is at its best in spring when the azaleas and rhododendrons are in full flower. There is also a famous Japanese garden.
Formal landscaped gardens near Wrexham in north Wales. Lovely summer bedding schemes.
University of Liverpool botanical gardens on the Wirral in Merseyside. A huge herbaceous border in summer a very good display of alpines in the spring and a large variety of other interesting plants. Very well landscaped on a hillside with panoramic views across to north Wales .
This is a country park near Bolton so is free to get in. The remains of Lord Leverhulmes terraced garden are very interesting and there are a large number of specimen plants. For those who feel fit there is a good walk up to the top of Rivington Pike.
A good site listing the many gardens to visit in Cheshire
A very grand name but a wonderful example of a Victorian town park. Very nicely laid out bedding plant schemes and woodland walks where there are a number of good specimen trees. There is also a cafe in the conservatory, a boating lake, a bandstand and a museum. The park is situated in Churchtown just outside Southport and entry is free. Southport is also the home of an excellent flower show in late August/September and is very good for shopping and seaside (when the tide is in) walks along the recently refurbished promenade.