We do know the law (better than you for sure) and we have broken none, so are not in the slightest bit 'worried'.
Obviously, as I am not privy to any of the commnications between you and any of your students I am not in a position to comment on who said what to whom. That is obviously between you and your writers. Obviously in this particular manner you and the writer are both making the same accusation albeit that M is making these through the posts of Serene. My comment on the Malicious Communications Act applies to all persons that have received such offence material, and will be regarded as a criminal offence for which prosecution is an option.
I very much doubt that you know more about the law than I do, but I am not here to compare qualifications. The information I supplied to Serene with regard to a possible course of action was contingent on her friend being able to prove the claims she is making. I agree that she is foolish to make such assertions if she is unable to back these up with evidence, however, from the tone of the posts made by Serene M was not supportive of her decision to make these posts, but was persuaded by Serene that this was an appropriate way of exposing you. If the allegations are false (as you claim) then Serene has indirectly caused a lot of problems for her friend.
You may have difficulty in pursuing a claim against M for libellous comments since she has not specifically made any declarations on here herself. She could rightly argue that these were not her opinions but the opinions of Serene and therefore she cannot be held liable for comments SUPPOSEDLY made on her behalf. If it were possible to pursue someone for comments made by another I could make any assertion on here stating that someone else had told me to make that comment knowing that they would get the blame for the comment. That is not how the legal system works. You can only pursue the author of the libellous offence, not someone they claim has asked the to do it as you have no way of proving that the other person asked the poster to make those allegations.
Given that this is a forum and names created cannot be associated with a particular author claims for libel or unlikely to be achievable as the poster is only identifiable through their email address, which does not have to even be an address that is in existence at the time of registering with the site. The moderator also has a duty under the data protection act not to disclose the details of posters on the sites and so therefore tracing a poster is nigh on impossible.
Yes you can take the action you propose and send the essay to M's tutor. What will this achieve? You will still not be able to take legal action against her as you cannot prove that she has had any direct involvement with the posts made by Serene. Surely your company would gain more kudos and respect by just accepting that in business you are always going to get a number of people who do not like the way you do business. The way you have conducted yourself on this forum shows a lack of professsionalism and potential writers are likely to be discouraged from applying to you for the way in which you have felt the need to expose details of one of your writers just because they have dared to accuse you of not being legitimate. If your company is as successful as you claim, comments like this would have little or no impact.
This is the same way in which academicknowledge reacted when being exposed for the exorbitant fines they levy which they eventually admitted to after initially denying that they charge 300%.
I am sure you would have got a better response if you had not publicly exposed the writer in the manner you did.