Not for me to provide legal advice, I'm afraid. But let me explain the options.
1) Do nothing. Some employers expect employees to do nothing because they think the employee does not understand the law or it will be too difficult, or involve expensive lawyers.
2) Pursue the case through an Employment Tribunal. This is relatively simple, a tribunal is a convened body of three people who interpret and decide upon the case based on the law. If they find in favour of the employee, they have the power to award damages, and (sometimes) to order the employer to re-employ. If the employer still won't do it, they can awrds more damages.
There are six 'fair' reasons for dismissal. Please understand that I mean 'fair' in the sense of legally fair - not whether it is just or not. The six reasons are:
Conduct
Capability
Redundancy
A statutory reason
Retirement of employee
Some other substantive reason
The most commonly used ones by an employer for dismissal are the first and third ones.
Conduct is easy to understand - you did something to break the company rules.
Redundancy can be confusing and is used sometimes by an employer as a 'cop out' to get rid of difficult staff. But your friends employer is saying she is not made redundant.
I won't explain the rest - she can read about them here: -
http://www.berr.gov.uk/whatwedo/employment/emp loyment-legislation/employment-guidance/page30 887.html#When_is_a_dismissal_fair_or_unfair_
From what you have said, this employer appears not to be acting in a fair manner. Some do it out of ignorance, some because they simply believe they will get away with it. If she wishes to pursue this, suggest the CAB in the first instance. It depends what she wa