Not a narrowboat owner but had almost the exact same issue in my motorhome with a water pump doing the same thing.
Nine times out of ten it's one of these:
- Wire gauge too thin for the run length — voltage drop causes the pump to work harder and draw more current
- Fuse rated too close to the pump's running amps — leaving no headroom for startup surge
- Partial blockage in the pump or outlet making it labour
Worth checking what gauge wire you've run from the battery to the pump and how long that run is. If it's more than a couple of metres and you've used anything thinner than 2.5mm² I'd upgrade it straight away.
Also, what fuse are you running? Bilge pumps can pull 2-3x their rated amps on startup. If your pump is rated at 5A and you've got a 5A fuse in there, that's your problem right there.
A proper inline blade fuse holder with the right rating sorted mine — picked up a Victron SmartShunt recently too which actually lets me see exactly what's pulling what, dead handy for diagnosing this stuff.
What pump is it and what's the fuse rating you're currently on? That'd help narrow it down.