I need to buy and fit a cooker hood. The cooker is on an external wall with a sloped ceiling. My problem is that there is only 1200mm from the hob to the ceiling, about 1100mm to the bottom of the suffit board. The roof has guttering along that edge so I couldn't vent through the suffit board which leaves me the 1100mm in which to fit a cooker hood. As the minimum recommended height from electric hob to cooker hood is 650mm and I'm fairly tall, I need a cooker hood with a good extraction rate (~500m3/hr) which can fit in 350mm. Can anyone suggest a cooker hood which might fit the bill?

Why not make your own, you will probably get a better result.
Take a line at 45 degrees upwards and outwards from the outside edge of each burner, and establish where the edge of the cowl should be. (the lower the better, but leave space for your head)
Buy an extractor fan, with a grease filter.....or accept it will get very dirty, and a closable lid/cover.
Think about where the air is going to come from, the air that you will blow through the wall along with the steam, burnt fat and oil.
An air vent, high up near the ceiling along the same wall is a good position as the incoming freezing air will have a chance to warm before it hits you. Fit an air tight cover to stop your warm air from disappearing outside, when you are not cooking.
An alternative is open a window - not recommended! You will freeze in the cross wind.
Or let the make up air come in through various cracks and holes in your home - this will cause drafts and cost you money having to heat all the cold air coming in, when your warm air is blown out when cooking.

You have not said what width of cooker/hob the hood has to cover. The old fashioned hoods like http://www.johnlewis.com/231326922/Product.aspx would vent straight out and will fit in your 350mm of remaining height. Venting 500m3/h is another story.

I am tall too and I like a hood with two bulbs (or more) but you need to keep your hood as low as possible otherwise it will suck more air than cooker stuff. Sorry I am not of much help.