Alternative to standard external fridge water filter

Hi,

We've just installed a new fridge/freezer with a plumbed water dispenser and ice maker.

It came with what I'm guessing is a standard external water filter cartridge - the kind that can be bought for about £10-£15 and needs changing every 6 months.

However, we're not very happy with the taste of the water and are wondering if there are any alternatives for better tasting water. As a comparison, we have Brita jug filters which we're very happy with.

Thanks,