There is absolutely no need to be worried about this.
I have managed 3 Radiology departments within hospitals and in all 3 hospitals GP's have not been able to refer directly to the department. If a GP sent a referral card it would be returned to him stating that he MUST refer to a specialist who would then refer if necessary. This is to ensure that unnecessary exams are not requested. e.g. if your GP suspected a bowel disorder he may request a Barium Enema. If you were referred to the colorectal service of your local hospital, who are specialists and see sympoms thousands of times a year, they may see this as unnecessary and send you for a colonoscopy (non-radiographic exam). They would also have your hospital medical records.
The only thing GP's would refer directly for would be broken bones in which case this exam WOULD HAVE TO BE CARRIED OUT regardless of how many you had xrays you had received before. Believe me, I have seen patients with a list of x-rays as long as your arm and they dont have any apparent negative effects. Knowing all I know about radiation, I would personally only become concerned if I were to get to, say, 5 or so CT scans. Anything other than this I wouldnt be overly worried about.
These exams are not given out without proper considersation so please dont worry about it. If you are given a radiographic exam it is for a very good, and proven, reason.
Dont worry
Natalie