It can be tricky to grasp sometimes, but it does need consent. The easiest way to start is to work out where your original rear walls are on the house, In this case you have a rear wall where the window is on the rear room marked "Reception Room" and a rear wall at the back of the kitchen where the door is. You also have a side wall where the Kitchen window is.
Your 3.5m rear "side infill" is actually a side and rear infill as it extends off both a original side and an original rear wall. If you are then adding extensions to this side and rear extension, you will have to ensure the extension is:
a) no greater than 4m (it should be a detached house from what your saying) from the original rear wall which is off the reception room. Your proposed extension will in effect be a 6m long side / rear extension and require consent.
b) not wider than half the width of the original dwelling (as RichA says). Because it's a side extension as well, and you in effect will be extending the full width of the house.
You could extend the kitchen back (on it's own) up to 4m if that's original, under permitted development, but if you want to link the infill extension to another extension, then they will be judged as a side and rear extension and both rules apply.