There are several types of health insurance - perhaps the main two being Private Medical Insurance (BUPA for example) and Income Protection.
One gets you your op. privately (although often in an NHS hospital and then being transferred to the private wards or a private hospital for recuperation and nursing care) and quickly.
The other pays you an income while you are off sick - usually due to major conditions and kicks in after a set period (say a month or three months).
They are full of exclusions and if say you went to your GP eighteen months ago with a condition you will be excluded for anything that is diagnosed (by a specialist doctor - not the insurer) to have resulted from it.
So you would be wise to disclose any gp visits, casualty experiences etc. because the insurer will check your records at point of claim anyway.
So if your heart failure is diagnosed as a result of your high blood pressure (that will be an excluded pre-condition) then you will not get your by-pass on the insurer because you take a half an aspirin a day to keep under control. If your knee - which you went to the doctor about last year and got some pain-killers - suddenly gives up the ghost and you need an op. then it won't be covered.
But if you develop a new condition - it will. Or a condition you declare that has given no trouble for say five years - no doc visits about it - then it probably will.