I handed my notice in this morning as I've got another job somewhere else. I've been here for three months and was told last week by my manager that as I was on probation I only had to give a week's notice. Now, HR has said I'm contractually obliged to work a month's notice.
How watertight is this?
I've landed a really good job that I've been hankering after for five years and they will not be happy at all if they have to wait a month for me to start.
Doesn't make any difference. Firstly as you've only been there three months they can get rid of you on whatever notice is in your contract anyway, and secondly you are contractually obliged to give the notice in your contract regardless of what comments/threats they have made.
It's pretty standard to have a month's notice so I'd be fairly shocked if your new job withdrew the offer because of having to wait an extra 3 weeks.
Why do you need to wait and see what happens? What do you think might happen?
Just check your contract when you get home and the answer will be there. If it says you only need to give a week, that's all you need to give. If it says you need to give a month then your leaving date is one month from today.