Fortunately, we live in a country where your private medical records are sealed. An insurer would only be allowed to access them with your express permission, and even then they can see specific information relevant to your policy. For example, they might want to know if you smoke or about any pre-existing medical conditions.
While you have every right to refuse, this might result in your policy not being accepted. Generally speaking, there are providers out there who do not conduct medical checks, so if it’s not something you are comfortable sharing, you should be able to get coverage regardless. If you’re happy to share, however, you just need to get in touch with your GP, to let them know and the insurer will get in touch with them.
As well as asking to see your medical records when you are applying, an insurer might also want access to them after you die. Generally, this will be if they are contesting because they believe that you died of something that was not included in your policy. Even in this situation they will need written consent from someone who is acting on your behalf.
In some situations, life insurers will share information if you are taking out a policy with another provider. But once again, they will need your permission to do this.