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With all due respect you are making an awful lot of assumptions. The previous employee may well have quit for their own reasons, you may not be invited to social events with this lady simply because she does not know you outside of work.
I doubt HR are involved liking someone at work is common and not a problem unless it affects either parties work. In any event I do not see why you feel you must leave simply because someone may be attracted to you.
If you do feel you must leave you simply need to give the notice required in your contract.
I hope this helps, please think carefully about what you do, jobs are not easy to come by and this does not seems a good reason to forego one to me.
What has she done to show she likes you and how is it being covered up?
Why do you feel you should have gone to hospital with your boss, have you done this sort of thing before with her?
Thank you for your reply
My feeling is that this is not organised but that these are individual actions. I think you boss is teasing and flirting not taking actions dictated by HR although she may have been told relations between staff are frowned upon as this is a common policy by employers as it can cause problems in the workplace.