Unfortunately, my experience is most GP's don't know a lot about miscarriage. Many are reluctant to investigate after 2, even 3 because the probability is you will still go on to have a subsequent successful pregnancy.
This doesn't make it ok. I had to practically beg to be referred after 3, and there are now only certain doctors that I will see in the surgery if I need to discuss this. My surgery has a website where you can check Dr's specialised training and interests. If you find one who is interested in reproductive health or family planning, see them.
I was referred to the RM specialist in the local hospital and had lots of blood tests - including thyroid function, hormone, iron, lupus, anti phospholipids. Be aware - for these tests to be accurate some need to be done on a specific day of your cycle, some you need to fast for and another must be a "fresh" sample. Mine weren't - I found this out after seeing someone privately so I have to have some repeated.
They will also likely order an ultrasound to check your uterus and ovaries. This is painless but can be a bit nerve wracking as they aren't allowed to tell you what they see - they take images and then it is analysed and a report produced and sent back to RM clinic.
If you are very lucky they may order karotyping. This is to check yours, and your partners chromosomes for any abnormalities that you could be passing on. I paid privately to have this test done, it was £350, but worth it to rule it out. If we did have any issues it would have likely meant IVF.
A really good to read "is your body baby friendly"