Today the Gunnersbury CIC posted this notice:
“Following Government advice and to protect our visitors and staff we have taken the decision to close Gunnersbury Park Museum and suspend public programmes and schools visits with immediate effect. We will continue to review the situation and will endeavour to re-open as soon as is possible.
Gunnersbury Park will remain open 7 days a week for the community to exercise walk the dog and enjoy the spring flowers. Our partners at Benugo will also be keeping the cafe open for all visitors. Please enjoy the Park responsibly, following Government guidance at all times.
And remember to check our website and Twitter to keep up to date with Park news.”

Subsequently the cafe has had to close to meet the government requirements. (update 26.03.20)