Thanks for the pointers here folks.
I live at the top of a hill, and whilst my garden is fairly enclosed, when a wind whips round it really whips round! I previously smoked on a corner patio surrounded with windbreaks and had no problem with airflow. I am not planning on a fully walled construction, the "walls" will be 4 ft high beach windbreaks - just enough to keep the direct wind off the air intakes. They will be a fair distance from the smoker so plenty of room for breeze to circulate I hope.
With regard to the sealant, I'm not proposing attaching the plastic roofing to the wall using sealant. I will be screwing a piece of timber to the wall, then screwing the plastic roofing to that. The sealant is to stop water running down between the wall and the roof, like flashing over a bay window. May not even be necessary. I'm not looking for anything fancy here, just a more comfortable place to do my cooking, with lighting etc, and not having to worry about leaving things out on the table and them getting wet. It would also suffice as a wood and coal store if I build it big enough.
As for sturdiness, that will depend on budget. It's gonna be one or two pieces of 9 ft timber driven down 3ft of earth and packed in perhaps with a little cement. The roof will be corrugated plastic roof sheeting - something like this, a few fitted together, with silicon sealant at the joins
http://www.diy.com/nav/build/building-m ... Id=9282572This way, it's cheap enough that if it proves unsturdy to the elements, I've lost fifty quid at worst.