Hi Kamil,
I'm a Brit too, living in Japan and I work in the travel industry. Sorry, but I don't know anything about Tokyo or Kyoto (my business is on a different Island). But I just wonder if you are used to traveling in the heat, because Tokyo is super hot in July and August and can also be very very wet in June. I understand that you may not be able to choose any other months to travel, or maybe the heat and rain aren't such a big problem for you, it's just something for you to think about.
The main thing is, Japan is an amazing place, whenever you come. Enjoy.