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I think most independent sites and some of the longer distance operators do - thetrainline and redspottedhanky both do and I believe Virgin do for their services.
I am not aware of any that allow you to specify anything though - all the ones I have used (which admittedly isn't many or very often) only go as granular as AM/PM.
We are aware of an issue with emails from the Forum to Microsoft-based email accounts (hotmail/outlook/live.com email addresses). This is being looked into currently, thanks for your patience meanwhile.