The type of hedge you plant depends on your location, lighting, climate, sun/shade, etc.

Depends whether its sun or shade to an extent, but something that only grows to 1 metre is difficult, as is containing the roots in something.

If you don't mind deciduous and its a sunny area, berberis atropurpureum 'nana' should make 2 and a half feet, otherwise, for evergreen, its Buxus microphyllus, which you'll need to keep trimmed. The depth of the box is critical - it needs to be a minimum of ten inches or a foot deep and about 9 or 10 inches wide. There should be drainage holes, and you will need to water frequently.

Is it not possible to grow in open ground along the length of the fence? Bamboo's comment about watering is the most important and could be critical. If for some reason you forget to water in the hot weather you could find the hedge struggling or worse.

Probably easier and more reliable to replace the fence with a taller one, or have 2 foot of trellis added along the length.

Bamboo might be an option here - it's evergreen and the height will depend on the variety you choose, but would remain stable. They are often grown in containers in order to restrict them as they can be invasive. Any container really needs to be a large as possible (what can you accomodate?), but as for watering, I would install a drip pipe - basically a leaking pipe - running along the entire length. You can fit a timer to it, fit it to an outside tap and Bob's your uncle.

Thanks All. I can't plant in the ground as it is concrete and I can't have a taller fence as its near a road. Planning are on my case so looking for an alterative to the 2m fence I have put up. I could have bedding up to 1m deep theoretically and possibly up to 10 inches wide. I hadn't thought of bamboo.

I don't know where you are, but bamboo is susceptible to cold in winter when in containers, particularly shallow containers, so if you're somewhere north, that should be a consideration.