>>2692749UK SW coastpath is good and missing from your map. Also London has several long distance hikes in it, in spirals, if you want to experience something different. You could stay at the same hotel and get public transport to/from each days start. It wouldn't be out-out, but you would get jaw-dropping views time (albeit brief) away from the noise in Richmond park hampstead heath etc, and experience a lot of culture along the way. You can make it strenuous by doing at a different pace to usual etc.
>https://tfl.gov.uk/modes/walking/top-walking-routes