Pretty much yes, you have to apply to each hospital/trust to get access to your records. It's usually free if you just want to read them but you can't get copies or take it away from the hospital. If you want copies there's a charge and it's usually about £50, possibly more.
You need to make the request in writing too. The website for each different trust should have a link about accessing your records with a form to fill in and contact details.
It wouldn't hurt to ask your gp in case they do have access to the information you want, but again they might charge for this.
It's true your GP can access a kind of centralised database with information about you, but it doesnt mean they can access absolutely everything. For example my GP in the past has been able to access my test results that I had done in my local hospital, but they couldn't access my whole file or any of my notes from other hospitals.
I work for the NHS in a hospital and we keep patients records on site. When someone is discharged from hospital all the GP gets is a brief discharge summary about the patient. They do not get sent any of the nursing notes and other documentation, we keep that. But the GP can access some of our databases to see x-rays, blood test results and other test results.