Been through almost exactly this on my boat last spring. Nine times out of ten it's one of three things:
1. Undersized cable run
Inverters draw massive current at 12v — a 1000W inverter can pull 90-100A. If your cable to the battery isn't at least 35mm² (preferably 50mm²), you'll get voltage drop and heat, which trips the fuse before the inverter even reaches full load.
2. Fuse rating vs cable rating mismatch
The fuse should protect the cable, not the inverter. What size fuse are you running, and what cable gauge? A lot of boat installations I've seen have undersized ANL fuses fitted by the previous owner — classic "that'll do" boatyard wiring.
3. Battery internal resistance
If you're on older AGM or flooded leisure batteries, they might not be able to deliver the surge current the inverter demands on startup. Particularly bad in cold weather on the cut. I switched to a Fogstar Drift 200Ah LiFePO4 a couple of years back and the difference in inverter performance was night and day — lithium handles those peaks without blinking.
What inverter are you running, and is it a pure sine or modified sine? Some cheaper modified sine units have horrible inrush characteristics that hammer the fuse on startup.
Also worth checking all your connections are clean and tight — a slightly loose terminal on a 100A draw gets warm fast.
What's your current battery bank setup? That'll help narrow it down. Others on here will have seen this too — @WaterloggedWatts had a similar thread a while back if you can dig it out.