It can get quite complex,as there are possibly two issues here-the 'inlet' could in theory be remote from the shaft/entrance to the building-but as there is likely to be multi pump attendance,this is not necerssarily an issue (i.e. one pump deals with suppling the water,another gets personnel & kit up the FF shaft.)Lets keep it simple though and assume that it is a dry mains,inlet situated near to the FF shaft-then BS5588 Part 11 (para 40.5.2)says that the max distance between Outlet at highest level and fire appliance is 30m-but only 'horizontal' travel distance has to be counted if there is a FF lift.If there is no FF lift,then both horizontal and vertical distance counted,with the stair sections multiplied by 150%.
BS5588 Part 5 will give some other examples,depending on type of use of building/number of floors,but for instance, access to a FF shaft,that is not on an outside wall,should be via a protected route and no longer than 18m.
So yes,there is a maximum distance that a FF should be expected to lug his gear,and I wish someone had told me that many years ago,as a proby I had to lug B.A.,FF equipment and two lengths of hose up 11 storeys once-and it was no Fun!