When a fuse blows , that is sign that something else is probably wrong, and whilst sometimes a fuse that is passing current close to its limit can weaken with age and sometimes it will break the circuit at what might appear a random time, if a new fuse blows straight away when the pump is connected, it points to the pump drawing more current than it should.
I suspect from your report the pump is damaged and is drawing more current which is blowing the fuse.
Submersible pumps used in caravans rely on water actually passing through the pump to keep it cool. If for any reason the water stops (E.g. the barrel empties, or the power to the pump is not switched of when the taps close) the pump can begin to overheat distorting the seals around the moror's shaft, and as the pump cools down a negative pressure develops that draws water into the motor housing. This usually produces a pump failure within a short period of time.
Never let you pump run for more than a couple of minutes, when the barrel is dry, or when all taps are closed.