As far as the dismissal goes, you cannot challenge it. That is because if you have been continuously employed at your place of work for less than 2 years then your employment rights will unfortunately be somewhat limited. Most importantly, you will not be protected against unfair dismissal. This means that your employer can dismiss you for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because you were trying to assert any of your statutory rights (e.g. requesting maternity/paternity leave, etc.).
If the dismissal had nothing to do with any of the above exceptions then you would not be able to challenge it and your only protection would be if you were not paid your contractual notice period, because unless you were dismissed for gross misconduct, you would be entitled to receive your contractual notice period. If you did not have a written contract in place you would be entitled to the minimum statutory notice period of 1 week. Your employer would either have to allow you to work that notice period and pay you as normal, or they will have to pay you in lieu of notice.
When it comes to defamation, such claims are extremely difficult to pursue. Many people are intent on suing for defamation without having any appreciation of the law behind them, so I will try and clear things up for you now.
First of all, certain conditions must be met for the statement to be classified as defamatory. These are:
1. The statement has to be untrue.
2. It must directly identify the complainant.
3. It must have been published, usually communicated to at least another person.
4. It must be in a form of words, which would tend to lower the claimant in the estimation of ‘right thinking members of society generally', expose the claimant to hatred, contempt or ridicule, or cause the claimant to be shunned or avoided.
5. Its publication has caused or is likely to cause serious harm to the reputation of the claimant.
Whilst it may be easy to prove that defamation has occurred, the legal process of pursuing such a claim is extremely complex and expensive. As this goes through the High Court, you would need the professional help of specialist defamation solicitors and the costs are undoubtedly going to run into the thousands right at the outset. Also there is no legal aid available for such claims so the complainant must fund these personally. So when you hear about defamation claims being made, these are usually pursued by big corporations or celebrities who have a public image to protect.
You must also consider whether the party alleged of making the defamatory statement can defend the claim. Even if you satisfy the criteria to prove the statement was defamatory it could be defended on a number of grounds, including by providing evidence that the statement was substantially true or an honest opinion.
There is of course nothing stopping you from contacting the other party and threatening them that what they have done amounts to defamation and that you will consider pursuing the matter further if they do not retract their statement. This could prompt them to reconsider their position, but I would not recommend that you actually proceed with a claim for defamation due to the issues highlighted above.
The police matter has also been concluded now and you have been found innocent – as you were not wrongly convicted you cannot pursue compensation against them.
So legally your options are rather limited unfortunately. I cannot advise on how best to try and turn this around but you need to try and seek employment where there would be no links to this period of employment, for example someone who would not be requiring a reference from that past employer.