May I please add to Justlead1's excellent advice?
Sometimes if your in older property, there can be screw-down valves on the system which have loose jumpers, that are designed to stop back flow, not all screw-downs of course some have fixed jumpers which are okay.
Unfortunately the loose jumpers valves can block the air from being blown back into the storage tank/cistern by the main.
With this sort of valve its "make it up as you go along" as to how to remove the air if the usual link over does not work.
I have had it work by feeding a thin hose, such as that used on gas manometers, down through the tank connector.
I have had it work by taking the ballcock adaptor off and connecting a hose pushing the other end down the tank outlets then turning on the water.
And possibly other ways as well. Such as corking the tank outlet and fitting a full bore gate valve further down the line, then removing the screw-down valves loose jumper.
That gives you a reasonably free path to blow the air back into the tank.
Its not as good as replacing the screw-down valve all together of course. But sometimes fitting a new valve to a tank can be a hard job if its old property.
What you are trying to do is remove trapped air, so any other ideas you come up with of your own are probably just as valid.
It may even work sucking on the top, instead of blowing.
Good Fortune!