Hello  Dave,  
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.