Which single direction should the top of Broughton Street allow motor traffic to pass when it's reduced to one lane to make space for the segregated cycleway?
Well, motor traffic can only head straight on to the Picardy Place roundabout at the moment, so that would be sufficient. It's only two marked lanes from after the entrance to Broughton Street Lane, so no great loss, really. (Or do you mean make it one lane in total, like what it is at the moment? Again, world not ending as I speak).
I suspect the main complaints would be from shop owners, as you'd presumably have to take out the (off-peak only) parking. However, the usual arguments would apply. Plus, imagine how much more of a high street and an attractive shopping destination Broughton Street would become with less space dedicated to motor vehicles.