If you live near west London then Kew Gardens is a great place to visit. It has all the elements of a garden on a grand scale. In the summer the gardening students each have an allotment plot to plan and manage so you can even pick up some tips for growing veg.
There is so much there for children, space to run around, fish in two of the glasshouses, a tree top walk, lakes and ponds and my favourite a huge badger sett where the children can run in and out of the tunnels. There is also a large indoor play area with a botanical theme, called climbers and creepers (suitable for 3 to 9 years old, though the littlies can still use it) and a new outdoor area yet to be tested as it will not be open until Easter. So we were there this half term spotting snowdrops and smelling the viburnum.
The Princess Diana glasshouse was hosting a colourful display of orchids, with a parallel craft activity at climbers and creepers creating exotic flowers, with paper plates and tissue paper. Quite an easy thing to do at home. We did go and look at the orchids but the biggest attraction for the children were the other new ( i think ) occupants of the glasshouse, lizards which are roaming around helping to keep the cockroach population at bay.