You don't have the right to say no or even stay silent. If you refuse to give up your passwords they will charge you with the whatever the legislation around it is, it's 2 years behind bars for refusing.
Probably not, just a waste of money and time, but hopefully someone can provide a reasonable recourse.
What if you say you forgot? I actually had times (after not having used my phone for a month or two) that I (& my muscles) forgot my PIN (not for the SIM card) and I had to do a factory reset.
Well it's not automatic 2 year prison sentence. The state charges you with a crime, it goes to trial, and then you have to defend yourself - if your argument is that you forgot, then it would be an interesting case - ultimately the prosecutor would need to prove that it's unlikely you forgot, say if they had proof (say CCTV recording at the airport) showing you using your phone 5 minutes before it was confiscated - it would be pretty hard to argue that in the space of those 5 minutes you forgot the password. But if you had a device in your suitcase and could successfully argue that you haven't used it in ages and the password was long and complex then yeah, I guess you'd be found not guilty - up to the judge/magister/jury depending on where exactly in the justice system you end up. But yeah, while stopped at the border saying "I forgot" is not a good card to play.
It probably won't end well but I'm curious what would happen if you give them a password that resets the device. Theoretically it unlocks it, it's just that it takes a minute and it's factory new at that point.
They'd charge you with destroying evidence, or "perverting the course of justice". They aren't stupid, they would know that you gave them a password that wiped the device.
An Immigration Officer may search you until they are satisfied you are a citizen. As long as you have a passport (or emergency travel document) listing you a citizen, this should be straightforward and they're unlikely to have grounds for any further search. At that point, you have been let into the country.
Customs Officers are much more likely to have grounds for a search — if they believe you are bringing prohibited material on the electronic device into the country (and "reasonable grounds" is low, as it typically is for customs — "you're acting kinda sus" is a reasonable ground), they can search your device. It is an offence to refuse a search, so while you've been admitted to the UK, you could be arrested for that offence.
This is all broadly comparable to most other countries immigration and customs laws; the UK is not an outlier here.
The problems with the UK are primarily things that apply to everyone, not just at the border — for example the Terrorism Act 2000 and Regulation of Investigatory Powers Act 2000. But again, in the border case — that's basically all going to be _after_ you are admitted to the UK.
Are they arresting you?
Because they have to let you in.