Morris Minor Owners Club

The negative terminal keeps producing a sort of fluffy powder. I'm guessing I should get a new battery as I don't know how long this one has been fitted. Are there different types of battery and what kind would I need?

A silly answer. Is your car pos or neg earth? Neg earth cars tend to produce less corrosion across the the terminals. I expect that someone will give a technical explanation. Greasing the terminals helps prevent corrosion.
As long as the battery is holding a charge then you don't need a new one. When you get fed up starting the car on the handle is the time to change it.

pour some boiling water out of the kettle dry off andput grease or vassaline on the terminals.

Electrolytic corrosion caused by flow of ions between mismatched materials - quite normal just clean and grease as above.....

If the terminal connector has rotted away badly - fit a new one before it snaps!

It's only recently started happening so it should be ok and I put some grease on. It's unlikely that I need a new battery then? Also it is wired negative earth.

Yes -unlikely you need new battery!

If the negative lead from your battery bolts straight onto the car then you have -ve earth, if however the -ve lead goes to the solenoid then you have +ve earth (assuming the battery was put in the right way around)