TheClogLady reading the debate, one of the concerns about buffer zones was that any restriction on rights to protest risks unintended consequences and potential seeping into other issues.
There also seemed to be some technical points on the actual policing of these zones that were probably pertinent, too - at almost all clinics protests aren't a problem, so making a blanket ban risks allocating resources that are sorely needed elsewhere. (I didn't quite follow all the discussions on these zones)
Also it seemed to be suggested that 'prayer' was one of the definitions of 'protest' to be banned, which seemed to risk making someone's inner thoughts possibly illegal.
I actually thought Fiona Bruce's thoughts were careful and nuanced. Despite her faith (and I presume a pro-life/anti abortion stance), she argued in favour of buffer zones for practical and compassionate reasons.