Celiac disease - getting baby tested?

[MandaLynn]

Could anyone let me know their experience on how to go about getting a baby tested if I suspect they are celiac/gluten intolerant? either NHS or private

Speak to your GP. It's a blood test.

Of course I will speak with the GP. I was more hoping for an insight into the process and others experiences. Is it easy to get referrals? Is it a long process? Etc etc

It’s just a standard blood test

Your GP will talk through your concerns and decide whether it would be appropriate to test - blood tests for babies aren't done lightly. How old is your baby?
Coeliac disease in young babies is very rare as you aren't born with it. It's an autoimmune condition where something makes the body start to react to gluten inappropriately. This can't happen until a) the child is eating gluten (which doesn't happen before weaning) and b) something goes wrong with your immune system to make it react this way.
That said, if there's a family history of it, it's more likely as you are predisposed to having autoimmune issues.
Whatever happens, don't remove gluten from your child's diet until you've spoken to your Dr. The child needs to be eating gluten regularly for several weeks for the test to be accurate and also there's a risk of not getting the correct nutrients when following a GF diet.