Is the heater meant to be this loud?

Is the heater meant to be this loud in a series 3?

Sounds a bit too loud. Could be the electric motor is about to give up. If it’s noisy and not blowing much air, could be a rusted heater cowling.

It sounds more powerful than mine - has someone fitted a better motor?

It is a little noisy. Sounds like the mouse wheel is catching on the casing. Probably a bit of thermal corrosion Removal and strip down probably needed. A nice dinner table job for a couple of winters evenings.
A good lube with some Castrol KY Jelly and she'll be good for another decade.

Long time since I owned a S3 but I don't remember the fan being that loud. Does it blow heat out though, that's the main criteria for a Series
At least you can get at the unit to repair it, unlike most other LR models

The motor circulates the air from the heater matrix to the inside of the vehicle. Suggest an inspection of the cowling. It’s actually a right b’tard to remove. Better to remove the external cover and grill on the wing, remove the cone foam channel and you’ll be able to see the metal fan. If you switch on you’ll be able to see if it’s rubbing the cowling. A bit of gentle hand pressure can centre it. The fan is fixed to a spindle on the motor secured by a small grub screw. You’ll need a long reach 3/4 mm Allen key to get it out. If you see corrosion or problems best to remove the cowling by unbolting it from the bulkhead.