In reply to Em66:
In Yorkshire Brimham has plenty of areas that are easily accessible with a buggy, probably the closest area in terms of feel to Font in the UK. Ilkley is also pretty accessible (it is often freezing though so beware!)
In the Peak Burbage is easily accessible off the main track, also should be possible to get a buggy to Robin Hoods Stride if using the parking on Cliff Lane.
RAC Boulders as previously mentioned. Also in North Wales Caseg Fraith, Idwal Cottage, and Parisellas Cave are all roadside.
Tanygrisiau (again in North Wales) is a little bit of a walk however it is up a steep tarmaced road so ok for a pram (note parking is slightly different location to the guidebook so you don't have to cross the river via a single track as you would from the usual parking). All the bouldering is directly off this road so easy enough to do.