This reply is a little late but in case you are still interested.
As some of the other people have replied, the two factor authentication is generally a bit
of a pain, and if there is an alternative available you can investigate that. But there is
sometimes not an alternative available. I don't have a mobile phone (yes , really) which
complicates things further. My wife has a mobile phone but it doesn't seem to be able
to accept SMS on the (very cheap) Japanese service she has.
However all is not lost, since for the UK it is easy to get a very cheap SIM that is a genuine
pay as you go. The company we use is giffgaff
https://www.giffgaff.com/ they will post your SIM
out to japan free of charge . They have various monthly plans (which probably won't be of interest)
and also one- month packages (which may be of interest if you are are going back to the UK for a visit)
but for two factor authentification you can skip these and just (once you have your sim) 'add credit' to your
account. You will then have a UK mobile phone number and the credit will then stay there - you just need
to use your account (e.g. by sending a single text) once every 6 months. We put 5 pounds on the SIM
about 5 years ago and we haven't used all the credit yet! This is what I use to do the two-factor authentication
on my UK bank account.
I think there are probably other companies as well - buying mobile phones is generally pretty easy in the UK.