As Dave said, the Mk1 turn signal switch doesn't support the horn directly. The horn push button is in the center of the steering wheel. However, there should be a purple/black wire among the 5 wires loom for the Mk1 turn signal switch.
First a couple of notes on horn wiring (without a relay). The horn is permanently "hot" via a purple wire. A purple/black wire leaves the horn and goes to the steering column. There it joins the 5-terminal plug of the Mk1 turn signal loom. A purple/black wire goes up the switch loom and at the top is directed to the brush that rubs against the slip ring. The slip ring is insulated from the column. INSIDE the steering column is another wire that is in contact with the slip ring. This internal wire passes through a spring and a nylon bushing and finally exits the column with a brass contact tip. That contact tip rests against a terminal on the center, back of the horn push button. There is another terminal on the pushbutton that makes contact with the inside of the hole in the steering wheel. The wheel is earthed to the car via the steering column. When you push the horn button, that switch completes a path to earth via the steering wheel itself. In short, the horn push button provides an earth path for the horn, not a power source.
I have heard that reproduction switches have used non-standard colors. The brown/black wire on your switch is likely to be equivalent to the original purple/black.
There should be 4 more wires on the switch. There should be a light-green/brown wire in from the 3-terminal flasher unit's "L" terminal. The green/white and green/red wires in the switch loom correspond to the right and left side indicators. Finally, there will be a light-green/purple wire connected to the 3-terminal flasher's "P" terminal. That wire goes to the indicator lamp on the end of the signal stalk.
If you are going for a retro conversion, you may want to spend some time considering how you will operate the horn. The Mk1 horn components for the steering column may be hard to find new or used. I have no idea how you would adapt them to a later column.