Both Local Authorities and Parish Councils can enforce Public Space Protection Orders (formerly Dog Control Orders) on any publicly owned land and have been able to do so since 2005:
"any land which is open to the air and to which the public are entitled or permitted to have access"
Defra booklet re Dog Control Orders.
It's worth noting that they have to inform dog owners in advance of the control order coming into force though.
"If the council plans to put a new PSPO in place, it must put up a notice and publish it in a local newspaper and on its website.
The notice must tell you:
where the new PSPO will apply, if there’s a map and where you can see it"
Public Spaces Protection Orders.
To challenge a PSPO once in place you have to go to the High Court within six weeks.
There's a bit more info on this site.
Another good site for Dog Law info.
Some cities are banning dogs from multiple parks and open spaces and other's have enforced blanket, 'all dogs on leads when on any public/council owned property' orders. Sadly there is no onus on them to provide alternative areas for off-lead walks, even if they enforce on-lead only across the whole city. 