Hi there, I'm also in the UK and have worked for the NHS......
If you feel you need a second opinion then you are entitled to one and can choose which hospital you go to via the Choose and Book system. I know the system isn't great and it takes a fair amount of phone calls and nudging, but you can get yourself seen at a different hospital. If you can find someone who has experience of "re-dos" then you can also insist on a named-consultant referral from your GP.
If the radiologist has confirmed reflux then you should be able to discuss this with a surgeon. Also, if the radiologist has proven you now have reflux and you are not on a PPI, does your GP think you should be on a PPI to protect your oesophagus?
I know your family history is worrying you, so if they don't want to offer surgery should they not be offering medication? Was your father a smoker or heavy drinker? The risk of cancer should still be very low for you, but I think everyone in your shoes would want to be proactive about reducing the risk.
Those are my thoughts....... hope it's of some help,
GERD (over 2 years)
Lifelong stuff: Food allergies/intolerance, eczema, asthma