Does the time difference between London and Tokyo change during the year?

Yes. Because of daylight saving time the gap moves between −9h and −8h.

When is the best time to call Tokyo from London?

There is no overlap between standard working days, so one side has to call early or late.

London is 8h behind Tokyo. This gap is not fixed: daylight saving time moves it between −9h and −8h during the year.

London

United Kingdom

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Tokyo

Japan

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A 9-to-5 working day in London does not overlap one in Tokyo at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
London · United Kingdom	Europe/London	UTC+1
Tokyo · Japan	Asia/Tokyo	UTC+9

What is the time difference between London and Tokyo?: London is 8h behind Tokyo. This gap is not fixed: daylight saving time moves it between −9h and −8h during the year.
Does the time difference between London and Tokyo change during the year?: Yes. Because of daylight saving time the gap moves between −9h and −8h.
When is the best time to call Tokyo from London?: There is no overlap between standard working days, so one side has to call early or late.