When the concrete has hardened start by mixing up the mortar for bricklaying. This can be done in a similar way as used for mixing the concrete. Adding mortar plasticiser will give a smoother mortar, making it easier to use. Use the mortar to lay a row of bricks on top of your foundation (1), buttering the bottom and edges of each brick. Constantly check, using a spirit level, that the horizontal and vertical surfaces are level.
Start with the corners of the barbecue structure, building them up at first, by three or four bricks (2) before attempting to build up between them. Use a string line stretched across the two corners to ensure that they line up with each other.
You will need to build brackets into the second and third row of bricks from the top of the barbecue. The lower set will hold the fuel tray, while the upper set will support the grill - it is important that you place the brackets ensuring the tray and grill sit comfortably on them, making sure they are level.
After you have completed every third row you should smooth the mortar (3) between the bricks to give a flush and pleasant appearance - this is called pointing. Dry lay a few rows at first to make sure you are happy with the shape and position before committing yourself to proper bricklaying.
Point the vertical joints before starting the horizontal ones, lightly brushing any mortar off the surface of the bricks. When you have reached the desired height you may want to cap the barbecue wall with either coping stones or hard engineering bricks in order to give a more durable finish.
You should leave the barbecue for at least 48 hours to harden before using it.