Hi tillymay
I know you are really asking about how to avoid your mum's threats, but two phrases jump out at me from your OP:
I believe it is what would make me truly happy
I have suffered from depression and anxiety in the past
I don't think from these you are ready to have a baby yet, as you are focusing on the "cute" part of having a baby and the quick fix of making you feel happy.
Not only might the hormones you have from pregnancy and birth, affect your depression negatively and severely, you need to be aware of whole picture - how your body might cope anxiety-wise whilst coping with severe sleep deprivation, for example, how your relationship will cope with the stress of a newborn baby and then child, coping with a colicky/reflux baby who doesn't sleep, for example, especially if your immediate family won't be supportive...what if you had more than one child, what if your child has medical issues? Etc. Etc. Etc.
I am aware I am being a mean in my comments but this doesn't sound like an ideal environment for a newborn and it has to all be about them.
What you could start doing is preparing for the future. Work with your Mum. Why does she not like your partner? What can she/you do to help? What are you doing to work with your depression and anxiety, as it doesn't just go away and you will need support in managing this when you do go on to have a family. WRT Social Services, Mumof3 is right. Yes, your Mum can call them, but if they see nothing wrong, they won't do anything after their investigations. If they do conclude that they need to intervene, then your Mum would have been right in calling them in the first place.
I hope you make the right decisions for you and your boyfriend, and ultimately, for any future child