Do I need planning permission (pics included)

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Existing detached house with neighbours either side. Neighbour to the left is extending at the moment and has had planning permission granted. I've sketched how the ground floor looks now and option 1 is what I want to do and option 2 is how next door plans look. Both single storey.

Additional info, the garden is northwest facing so the sunniest spot in the evenings is where next door have put their utility room. I think its better to just have an insulated garage with plumbing and electrics and a big patio in this corner. Also my plans don't extend as far, just enough for a decent living area and dining table.

So it seems to me that both options are permitted development, although the neighbours are having some timber cladding put on the front and adding an upstairs window at the back which we would also like to copy. Is that why they've had to get planing permission?