You said in this thread and your other thread that London water is hard as rocks, but you're going to need to know the actual parameters if you plan to use RO. For this you will need a pH, gH, and kH test kit, and a TDS meter if those readings are important to you. Stable parameters are important because huge swings in pH or hardness could stress your fish and lead to problems. The only way to have stable parameters, especially when dealing with mixing or reconstituting RO water, is to test it each time and make sure it falls within the same desired levels.
RO and HMA membranes accomplish two different things.
RO membranes strip basically everything out of your water, including all the minerals and trace elements that cause your hard water. These membranes produce waste water at varying volumes, depending on the membrane you're using and the water pressure of your source. Some are pretty good with a ratio of 2:1 (waste to pure) but I've seen them go up to 4:1. This makes RO expensive if you're running a large tank, or multiple tanks, and you are using municipal water supplies that charge by the gallon. The product of an RO unit is pure water (or, at least, mostly pure). Unfortunately, pure RO has to be reconstituted to add back some of the essential elements and minerals required by your fish. This can be done by mixing it with a percentage of straight tap water until you get the desired pH/hardness/TDS, or by using commercial products like Kent RO Right or Discus Essentials. Test kits are going to be important because you need to know what your tap water readings are, what your RO water readings are, and what your desired readings are for the tank. Since everyone has different water and every RO unit/membrane is a bit different, no one can tell you how to mix the water to achieve your desired parameters. This is going to require some experimenting. For instance, a lot of people will start out by mixing 3/4 RO to 1/4 tap and then checking parameters to see where they end up. Then you adjust the percentages until you find the numbers that work for you.
An HMA membrane only strips out heavy metals, lead, VOCs (volatile organic compounds), and chlorine/chloramine. It does not alter your water hardness because it does not change the water's mineral content. This means that if you are using an HMA filter, your pH/hardness will be the same before and after. Most people use HMA filters to ensure they have very clean, chlorine-free water. This water does not have to be mixed or reconstituted since it retains its mineral content. HMA membranes do not produce waste water like RO units do.
Regardless of RO or HMA filtration, all water filters of this type must be attached to a water source. They can be plumbed inline to a cold water tap in your house if you want to mess with that, or you can hook them up to a garden hose in a garage, etc. Most hobbyists using RO water collect the pure water in barrels or storage bins, then mix it with tap or reconstitute it with minerals until they get the desired water parameters. Then you can heat and aerate it for 24 hours and use this prepared water to do your tank water changes. In most instances you would not go directly from the RO unit to the tank. I know some people have RO drips but this still requires the unit to be plumbed somewhere in the fish room, and you still need a place for all the waste water to go. A lot of people run the waste water line outside to water their gardens and houseplants or they collect it and use it for growing out hard-water fish like African cichlids.
The unit you linked to says it's RO or HMA, so you'd use one or the other. Since your objective is to soften the water, you'd be using the RO membranes. The HMA will not achieve that for you.
RO is definitely more work than typical water changes but once you get it down to a routine it isn't that bad. The real downsides for me are trying to find a place to set up the unit itself and then finding a way to hide the storage barrels in my fish room. This is why a garage or a basement converted into a fish room works great. No such luck here, though.
