Select the two endpoint you want to join, open the Pathfinder panel and click the top left button to join them.
You could draw this as one line with the Pen tool....
Sorry for the late response.
Using the Join function doesn't work because it changes the angle of the lines if the lines overlap or adds in a third line if there is a gap. I want it to extrapolate the ends of the lines out until they meet at a common point but I can't see how to do this.
I had considered using the pen tool as a last resort.
Following on from Peter's suggestion of using the pen tool, I figured the easiest way of doing this would be to make sure the diagonal line was drawn first and positioned accordingly, then use the pen tool to add another line. Holding down Shift allows a perfect horizontal line to come off this and then extending the end point of the horizontal or vertical is as easy as selecting the end point and using Shift + mouse drag. The vertical height of the horizontal line can be adjusted by selecting the joint and line endpoint together and Shift + dragging diagonally; thus maintain the angle of the diagonal offshoot.