HR will of course deal with it - I am an Employee Relations manager and these situations are our bread and butter.
1.Firstly, someone alleging that you smelt of alcohol is not 'evidence' - it is your word against hers.
2.Secondly, you were not actually working that day so you could legitimately have been as drunk as a skunk!
3.* *Join a union TODAY (you should be able to do it online) - they may or may not be willing to represent you because the situation is already ongoing, but they will still advise you.
4.Raise a complaint (informally for now, reserving the right to go formal) against this person and say that you do not want to work alongside them while your complaint is investigated.
5 Make a note of all the false allegations this person has made against you
Include any interactions between you that could be considered negative
6 Note any witnesses who could verify your rebuttal of the allegations
7 Just in case all else fails, make sure you have legal cover on your mortgage if you have one, because they could fund a case for constructive dismissal in the future, should it come to that.
8 Ask your employer for their policies on bullying, Dignity at Work and Grievance
If the allegation is false, which it seems to be - let your accuser prove the reverse! From what you are saying she is a horrible piece of work!