All travel policies quotes assuming all of the people travelling are in perfect health, they also assume that anyone not travelling who the travel plan depend on eg a business partner or immediate member of the family are also in perfect health.
If any of the above people are not in perfect health eg they have existing medical conditions any claims as a direct result of the medical condition will be excluded eg Medical or Cancellation claims. If you ring and declare the medical conditions they will advise you if they will offer cover, if there is any extra premium or bigger excess. If you accept this and pay the extra premium if applicable you will be covered for any claims as a direct result of it providing you have given the correct information.
Please bear in mind that they will consider taking aspririn to prevent heart problems and blood pressure tablets as an existing medical condition so you should declare it.
Most Travel Insurers will offer cover for minor existing medical conditions whether it for the people travelling or not travelling. If you are having problems getting cover there are specialist Insurers who offer cover or alternatively if its a heart condition try the Heart Association as they will have a scheme with a sympthetic Insurer and the same the cancer assoiations for cancer sufferers etc etc
Travel Insurance does contain a lot of small print, but if you are honest with your Insurers and read your policy so understand what it covers and more importantly what it does not cover along with any expectations they have for you your should not have a problem. Please remember cheapest is not always the best especially with Travel Insurance