I have been through this many times. Firstly it's helpful to understand the mechanism behind health anxiety. All anxiety is the result of perceiving a threat to your survival. The thing that most anxious people then naturally try to do is control that threat. Cancer is a massive threat to our survival, and, beyond living healthily and being vigilant for symptoms, we cannot control it. That's naturally quite terrifying for an anxious person, who tend to ramp up the 'vigilance' in an attempt to stay in control.
I have found certain questions/thinking patterns which are helpful to me when I'm in this state, for example:
Am I this worried about others?
Am I spending my days worrying that my mum/friend/boss/David Beckham has a secret cancer they're not aware of? If not, why am I doing this to myself? Try to act rationally towards the likelihood of cancer in yourself the way you would towards anybody else in your life. Try to tell yourself what you would tell them if they had similar concerns.
Acceptance
Sometimes the only thing to do when faced with a fear is to face the fear head on and accept it. What's the worst that can happen? I will die. Which is going to happen to us all some day anyway. I have had the good fortune already to live a longer, and a significantly better life, than many people in other parts of the world and indeed this part of the world. We all take risks every single time we leave the house and could equally get hit by a bus tomorrow. Which leads on to...
If the worst did happen, would I have wanted to spend my healthy years like this?
Anticipate what you might regret if you were suddenly gone tomorrow. Certainly number one would probably be spending your days fretting and worrying rather than just enjoying your blessings. If you suffer from a hyper-awareness of death, try to 'flip it' so instead you see it as a duty to yourself to live life to the full in case anything does happen, instead of fretting about what's going to happen and when.
Avoid the news
I don't read stories about cancer or premature death or even really death at all. As the news doesn't report about every person who lives a long, full life, or gets a serious illness but recovers, it represents a skewed view and will only feed our anxieties further.
Its all ultimately about letting go of the need to control your health to an impossible extent. Take care of your body, visit the GP if anything worrying occurs, take any offer of routine checkups or screenings, but otherwise accept the remainder is out of yours and everybody's control and take hold of your blessings in life and cherish them. Good luck 