Hi misalda, sorry for the late reply. How has your in-tank filter been? It certainly
looks like the type Jim S says is okay but I don't know if it's the salt-regenerated type, but maybe the shop can help on that. Either way, I don't think it'll remove chlorine, though.
Since your tap water is already soft and you only want to remove the chlorine, you could fit one of those sub-£100 'under-sink' filter systems you see in DIY places, Screwfix, etc with an extra little tap on your sink/worktop.
They're fairly easy to fit for a DIYer. All the ones I've seen just contain carbon (either carbon-block or granular activated charcoal) which will remove smells and tastes without affecting the hardness or acidity. I don't know if any jug filters are carbon-only, but might also be worth a check.
Or you could pre-boil water to get rid of the chlorine and let it cool down again. But that's starting to be a bit too much hassle
Tesco's cheap Ashbeck mineral water is another option and should be fine since it's a little alkaline and not too hard. But it seems a shame to have to buy-in if your tap water is already soft enough...