GP practices can't remove you from their patient list for just making a complaint and are required to investigate and respond to you.
They have strict rules regarding removing a patient from their list, one of them is breakdown of relationship, but this is still quite difficult for them to do and they would have to show evidence that the relationship has broken down between the patient and the surgery. Potentially a serial complainer could fall under this category if there was repeated, unfounded or malicious complaints, but it would usually take a lot to get to that point.
Your surgery should have their complaints policy on their website with details of how to make a complaint to them and their timeline for response.
Hope that helps.