When tungsten filaments are cold, they have very low resistance. It rises rapidly as they warm up, but for that first instant they draw a lot more current than the rating for operation. Tubes or light bulbs, same deal.
Tube manufacturers used various approaches to what was sometimes referred to as "controlled warm-up". Some worked better than others.
I would suggest trying slow-blow fuses of the correct rating with the Mullards. I would be surprised if this did not solve the problem.
As far as what risks, if any, you are running by using fuses of a somewhat higher rating, that would be a question best left to Doc and/or Paul I expect.