Offered the opportinuty to become supervisor, but it wasn't true

She is very upset with the whole situation

Totally understandable. Sorry for the situation.

she has been somewhat manipulated into believing she had a position she does not hold

Again, quite unfortunate.

she has effectively been demoted

Now, that is already quite not really true. She was not promoted, she was just tricked into doing work above her contract (and skills).

What can she do regarding this situation?

I will mention a few alternatives. Others might exist.

• MANDATORY: keep calm and polite in all situations;
• MANDATORY: keep any and all documents (printed or electronic, including e-mails); they might be needed later; be careful to not leak information out of the company;
• Just accept the situation. She did not really lose anything - except for doing some work not mentioned in the contract. Ego can heal easier than the body, if given the chance.
• Decide to leave the company and find a new job. Drawback: the new company might not be ideal either.
• She already went to N+2. She can ask him for some guidance. She can also inform him that her supervisor (N+1) gave her the opportunity to leave. She might not receive anything useful, but she might receive some interesting idea. Do not keeps hopes high, N+2 already was relatively dismissive.
• Talk to the work union - which probably does not exist.
• from the comment of @PhilipKendall (I am not familiar with the UK laws and institutions.): "Given this is the UK, the Citizens Advice exist as a free service and one of the things inside their remit is employer-employee disputes."
• Consult a lawyer knowledgeable in labor problems. Hopefully you will not get to court.

The most important thing is actually that she must decide what she actually wants.

Bonus alternative:

• Talk to the supervisor (N+1) about the actual possibility of promotion. Create together a roadmap, update the contract with the decision. He will probably not be happy - I do not know if he can just fire her easily.

I'm not familiar with UK law. But the following facts stick out as nearly unprecedented IME:

• You have a written contract, but are told flatly, "her contract does not stand"
• You're being handed a prewritten resignation letter
• You're told, "going to H/R would likely make the situation worse by taking it out of the managers hands"

None of that makes any sense. In particular, how much worse could it possibly be, versus being forced to resign immediately? Maybe worse for the managers. First steps I'd recommend are:

• Carefully keep all written contacts, especially that contract
• Do not sign anything, especially that resignation letter
• Write a letter to HR immediately and report everything

Main question she needs to ask herself

What am i looking to get out of this?

Based on that question there are things she can do, but every action have a reaction :)

How far she is willing to go to achieve her goal?

Potential actions are:

• employment lawyer
• HR report
• Glassdoor and social media posting
• Face to Face confrontation with person, promised the position
• etc

Regardless of the path she will choose, validity of her claim will very much depend on what proof she can provide.

Are there any tangible evidence to support it?

Good luck and keep us posted if possible