This question had us scrabbling back to the new planning regulations that came into force in England and Wales in October 2008.
Outbuilding Planning Regulations
Our gut feeling was that the regulations are intended to apply to the most forward part of the building, which is usually the house, but we needed to make absolutely sure. Your case is unusual in that the most forward part of your property is a high wall, whereas usually there is a low wall or no wall at all.
In fact the salient point seems to be not the closeness to the highway but the reference in the outbuildings section of the planning regulations to the wall rather than the boundary or highway. It states that no outbuilding “should be on land forward of a wall forming the principle elevation.” This seems to pretty clearly indicate that you can do what you like behind your own wall.
The only other restriction that we could find that might be relevant is to the height of the outbuilding, which you mention in your question. This is three metres (or 2.4m at the eaves and 4m at the apex for a pitched roof) but note that it drops to 2.5m if the outbuilding is to be within two metres of a boundary. You will need to check the height of your chosen summerhouse to make sure it meets those restrictions.
The height of the wall, although it plays no part in its effect on planning regulations for building work, would play a significant part in any discussion with the planners because it means that the proposed outbuilding would not be seen, and visual impact is one of the major factors in planning decisions.
Putting an obviously temporary building (as opposed to a building with foundations, solid walls, plumbing etc) behind a wall that high, which has been in existence for such a long time, would surely pose no problem whatsoever for the planners.
Ask For Planning Advice
If you are at all unsure, you could certainly contact the planning department at your local council offices to find out. They probably won’t be drawn on a specific question like this without knowing more about the project.
But you will be able to write to them with details of the project, including pictures of the proposed summerhouse if you have them, and simple plans of the property showing the location of the summerhouse. They will then advise you as to whether you require planning permission or not.