Take them to court.
What they have done is illegal, they cannot block your right of access even if it was on "their" property.
As for the communal garden, if it's on the deed as being yours to use, then you can use it.
The Citizens Advice Bureau will be able to help you out with next steps.
My mum told me of times when she had the worst neighbours in the world. They had a feud going on for years about right of access and this person was in control of the whole village.
It eventually came to a head by my mum pouring weed-killer all over their lawn, and the neighbour said that she wouldn't have bothered with all this, if she knew it was going to be this much hassle.
I'm not saying you should pour weedkiller on their lawn, but don't take any sh*t from these people.
It's surprising how many people back off if you stand up to them.