I work in a GP surgery, and the replies you have had so far show the variety in response you can get from surgery to surgery. This is not a stupid question and I wish I'd thought to ask it and bring mine when I moved over.
But the basic process that all new patients registrations should go through includes a summarisation of your medical record (or a review of an exisiting summary at the very least). In larger surgeries this is usually not done by a doctor, but by a summarising administrator. This then gets coded onto the surgeries clinical computer system so the doctor can see at a glance if you have any active or past significant problems. If something is seen when your record is summarised, you could be called in for review to make sure all is well. The level of summarising varies from surgery to surgery, in ours we enter significant past test results to either establish a baseline or record past abnormals.
So if you have any problems it is in your best interest to bring as complete a record as you can. I agree your immunisation record would be important. One of the most wonderful things about the NHS/National Health Service is your medical record gets transferred from GP to GP if you move, so it follows you for life in the UK and is complete. For UK citizens it's compllete from cradle to grave. All hospital and out of hours attendences are reported back to the GP, so they can react if necessary, and the report is added to your file. The UK is ahead of the USA in that some GPs can share your electronic record with secondary care so if you show up at a hospital and give your permission, the hospital can see your history, current meds, and past test results. It's a wonderful sytem when it works!