Image caption The Good Counsel Network says women are not being offered enough alternatives
Rival campaigners gathered outside the council building while the vote was taken.
More than 300 people wrote to the council describing the pro-life protesters as "intimidating and harassing", while those against abortion have said women are not being offered enough alternatives.
A report presented to the council cabinet concluded that, following unsuccessful attempts to negotiate an informal "safe zone" near the clinic entrance, a public spaces protection order was appropriate.
The report also states the "continued deployment of policing resources" outside the clinic was an "unusual and unnecessary use of local policing resources that could be deployed elsewhere".
The decision could pave the way for other councils to follow suit.
Elizabeth Howard, a spokeswoman for Be Here for Me, said: "It's what we expected, after really what can only be described as a sham consultation by the council.
"We're here to support women who maybe feel they don't have any other choice than abortion and don't want an abortion."
Council leader Julian Bell said he felt the cabinet had done "absolutely" the right thing.
He said: "I believe that this is something that's long been needed, so it feels good that we are actually breaking the ground with this and leading the way.
"I'm personally a practising Christian myself and so I think it's important to recognise that this is about protecting women from harassment and intimidation."
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