Maybe a mast collar? Does this mean that you have no boot to seal the hole where the mast goes through the deck or cabin top? You really cannot get "a lot of water" down the inside of the mast even with lot's of miscelaneous holes, but quite a bit of water does run down the outside mast walls and will flow quite happily into your bilges if you don't do something about that.
I don't really like the pour in place mast wedging systems though some folk do. They can make for a real pain stepping and unstepping the mast and they are not watertight so you still need a boot. There are rubber boots that are suitable for plastic boats with tin masts and are very easy to install. So if no boot, try that first. May be about 99% of the problem right there.
G'luck
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