Unsupported, that span of wood is going to bow. If it were me, I would have the sawmill cut the piece really thick. Then, I would route channels on the underside running the length of it. I would then put steel supports in said channels. The steel supports would then be what is mounted (however you plan to mount it).

HI -- Just something to think about .... So you are planning to have a bar/counter span across between the brick sides ??? So sitting facing out to the neighbors on stools and then everyone can look up your skirt/shorts/house coat ??? Sounds interestingly entertaining for the neighbors . Have a metal frame /skirting with brackets on the ends and the wood can be attached to the top. Screwed from underneath . I think you should have a railing of sorts .

Looks to me like you already have a privacy issue. Before I was doing that I would be investing in tall growing trees.to block the view from the neighbors upstairs windows.

Thanks for the advice guys, we planted gracious bamboo so give it another 6 months we should use a pretty dense hedge that's about 6 meters high. The fence is about 2. Can't wait for spring. We planted them about 1m apart so they can fill in the space quickly.

They only been in for 8 months and we're currently in winter so they'll resume their maximum growth rate when it gets warmer in about a month.

Sounds like I need to source for some structurally sound steel bars to hold the piece of timber up.