Sounds like good advice from above. I had a spectacular job done. I was so unimpressed with my internal builders I went to Wandsworth Borough Council for my external builders and building restoration names for this kind of work. I used Doug MacMahon: (the only builder I have ever used that kept on top of me rather than the other way round):
https://mahonbrickwork.co.uk/
I went to see three different properties he had worked on before taking him on. He cost an arm and a leg but I still get compliments from passers by when I open my front door.
Read his website about pebble dash removal.
A line from his website
To suit all budgets, we offer three different types of lime mortar pointing, all offering the same high standards of protection and weatherproofing.
DM me if you want the name of my street or to see the work.