Why not one-time use codes (e.g. [1]) instead of the phone? You can discreetly destroy the list that you carry as long as you can only get a new list at your destination.
The alternative - and much more practical suggestion - is not to travel with the codes. You run the risk of not being able to connect to the service - but at least no-one else can.
The most practical way to use this for non-2fa sites would be to have an overly long, random password and save it in the browser's password manager. Delete the Firefox profile before you travel, and you can't be compelled to reveal the password you could never remember.
An easier alternative might be using Deniable Encryption (http://en.wikipedia.org/wiki/Deniable_encryption)
By destroying the OTPs you are a: provably preventing access to the content (2 year or 5 year jail sentence)
I doubt the law is that strict. Do you know what level of suspicion or proof for the court to apply jail time?
However after reading about section 49 for the last few minutes I did not spot what the burden of proof is for non-compliance, the range of penalties for non-compliance nor how it scales with offense, and I do not now what "on reasonable grounds", a requirement to use section 49, means in UK law.
Another interesting quote is that inorder to issue a notice you "must describe the protected information to which the notice relates;" What counts as describe in UK law? I would hope that authorities would not just beable to guess at the structure. I would hope they are require to have some other evidence that would allow them to describe the information they are seeking.
I genuinely do not know anymore.
I knew that anti-terror laws were being broken every day in this country.
I never imagined it was going to be as flagrant as detaining the husband of a journalist as he changed airplanes in the UK.