Just to let everyone know, I finally got a proper answer from the embassy in London today (After calling and asking 3 times, one of the phone operators had the bright idea of going and asking someone who knew about it)
They said that as long as the work has nothing to do with Japan and all money is earned etc in the UK and working is not the purpose of my trip, then it is fine to continue any work required of me in the UK via the internet on a temporary visitor visa (Or whatever the 90 day stamp in the passport is called).
I just thought I would post that just in case anybody wanted to see what the embassy themselves told me.
Once again thank you all for your time and advice
