How can I attach a Pergola/lean-to to a pebble dash wall?
I would suggest fastening a piece of wood horizontally across at the top, and then fastening your shelter to that.  Using the appropriate fastenings (for either wood or masonry) to fasten the wood to the house.  This would only leave two or three holes that need to be patched if your pergola/lean to was removed.

Don't chisel any stones off the wall.  It will be unsightly and a difficult repair if the pergola is ever removed.

Before you proceed, make sure it is not against your housing association rules...