Hi Pauline
I'm new to this forum but saw this post and it resonated. I also live in a first floor flat in Dulwich and recently had the same issue as I wanted to install an irrigation system in our garden but don't have my own outdoor tap. I contacted Niko the Plumber who has been recommended a plethora of times on here. He came out and advised that he could install a pipe running from underneath our kitchen sink and through the external brickwork of our kitchen and down to the garden. He did all this very precisely, neatly and efficiently and we've had an irrigation system up and running perfectly for the last few months throughout our garden that runs twice a day. I'd wholeheartedly recommend you get in touch with him to discuss and you can say that the "King of Underhill Road" recommended him!
Plumber: Niko
Telephone: 07818 607 583