Its always a good idea to check with your council. The regs vary greatly. These days many no longer allow a gallows bracket to be used. Some allow a gallows bracket but only if the chimney breast on the adjoining wall was intact. Party wall agreements also come into play.
I think this guy must have set up his own contracting business in Kent.
He obviously worked on the terrace we bought 2 years ago.
First he removed the chimney breast in the kitchen and 3rd bedroom. Didn't seal it properly so the stench of the neighbour's chain smoking permiated those...
Since you have recently dug up the ground where the decking is to go, I'd suggest putting down landscape fabric to stall any weed growth under the deck.