Lexicos Focus on the bicarbonate level on the water bottle, the hardness will fall in. About 50-80mg/L bicarbonate is recommended. The waters you mentioned previously are about the only practical choices in the UK in bottled water.
Soft water, with no alkalinity can be corrosive, so you want a mineral level that controls scale and also limits the chance of corrosion.
Water with the bicarbonate levels above should give clean tasting coffee, but if all your coffee is on the sour side, and you are sure that you are not under-extracting, then aim at the higher end of the range. (No bicarbonate can give thin, bright coffee at a normal extraction, very high bicarbonate will flatten acidity & give the coffee a heavy, dull body.
If you are remineralising your water, you will need an alkalinity (AKA KH, or temporary hardness) drop kit to test & ensure you are on target (40-60mg/L as CaCO3).