You sure can

) I did in November & it was just perfect!
You are best off calling your local council to check for fees & other bookings. If you are not booked in & another couple is, you unfortunately will be asked to leave. Parks also have restrictions on what you can take such as rice & paper for confetti & glass objects (such as wine glasses beer bottles etc) The park I married in would not allow us to have our ceremony in the flower garden as it is sacred grounds to someone or other so that would be another good reason to call your local council!
Also by booking yourself in will also allow you to have access to electricity for the celebrants microphone

)
It also helps if you book to keep the public at bay & out of your photos ;o)