Not as such but you could ask the question as to whether you are being made redundant in favour of the new person. If so then you have a case because clearly the job is not redundant. Maybe they are just getting and additional operative for your job as a opposed to a replacement.
Thanks for that. It's not for me thankfully, but a colleague started here last December so, basically, does not have a lot of "rights" but I would have thought she should have been made aware of their intention to get rid! I know that is their intention, it's a very small office
As you seem to have concluded yourself, the person has no rights in a legal sense (because they haven't been there for 12 months continuously), but it is poor HR practice to treat any employee in this manner.