UPDATE 22 March 2020: Most gardens are now closing entirely and the nation is being advised not to go out unless it is necessary. This list will be updated as we get news, but people must now avoid going anywhere unnecessarily. Keep to the social distancing advice.
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English Heritage gardens
The English Heritage has announced all its pay-for, staffed historic sites are shutting, but that its free-to-enter sites will continue to be open. Free-to-enter sites include
Abbotsbury
Acton Burnell Castle
Ambleside Roman Fort
Belas Knap Long Barrow
Binham Priory
Blackfriars
Donnington Castle
Garrison Walls
Grimspound
Read the full list of sites open here.
Hepworth Wakefield
The gallery is closed, but the garden remains open to the public.
Hauser and Wirth Somerset

The galleries and restaurant have temporarily closed.
Chatsworth

The garden house, farmyard, adventure playground, gift shops and its restaurants will remain closed until further notice.
Bristol Botanic Gardens
The garden is now closed until further notice.
The Garden Museum

The Garden Museum is now closed.
Fibrex Nursery
Now closed but with an excellent mail order service.
Belvoir Castle
Closed in accordance with government advice.
Hestercombe House
Hestercombe House is now closed.
Yorkshire Sculpture Park

Closed until further notice.
Special Plants Nursery
This is now closed to the public.
Forde Abbey

The gardens, cafe and house are all now closed until further notice.
Oxford Botanic Arboretum
The garden and Arboretum are now closed.
Petersham Nurseries in Richmond

Richmond and Petersham Nurseries in Covent Garden are both now closed until further notice.
The Lost Gardens of Heligan

The garden has made the decision to close until further notice.
Chelsea Physic Garden

The garden has now been closed to the public.
Kew Gardens
Kew Gardens is closing from now until further notice.
Wakehurst
Kew Gardens is closing from now until further notice
The Eden Project

The Eden Project has now closed its site to the public.
RHS Gardens

All RHS gardens have now been closed until the foreseeable future.
Note: the RHS Libraries have closed until further notice.
Barbara Hepworth Sculpture Garden
Closed until 1 May.
Edinburgh Botanic Gardens

This has been closed to the public until further notice. The same goes for Benmore, Logan and Dawyck.
Arundel Castle
Arundel will now not open to the public from 1 April and will remain closed until further notice.
National Trust gardens

The National Trust's most recent statement is that it is closing all its gardens to the public. It's nature and coastal areas are still open as usual.
National Garden Scheme
The National Garden Scheme has announced it will be closing all its garden events and open days until the foreseeable.
Beth Chatto Gardens

The garden has made the decision to close until further notice.
Great Dixter

Great Dixter is due to open on 28 March and at the moment that is still going ahead but in a reduced way, with social distancing measures being observed. Check for further updates. The shop and nursery are still open for mail order.