Buy it. On a US-based heating forum
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, they occasionally mention the use of anti-freeze in heating systems. The water used with the anti-freeze can have a small maximum amount of dissolved solids. If the local water supply is unsuitable they will buy de-ionized water to fill the heating system. The price mentioned was, I think, about 10c per gallon.
This being the UK, I doubt that you'll find a supply at a similar cost, but I think buying commercial quantities would still prove to be be a lot cheaper than making.
Britas filters will not be effective. They may remove some of the dissolved solids, but they are not deionizers.
Also read the manufacturers' instructions. The equipment might tolerate softened water. If so, the dissolved solids will stay in solution and can be removed by occasional draining and rinsing of the steam generator vessel. Some equipment makers don't recommend using softened water.