There are two basic types of water softener - one which has a single cylinder and one which has twin-cylinders. You will be aware that the softener needs to "regenerate" every so-often when the resin becomes "used" and this is done by passing salt-water through and then rinsing.
With a single-cylinder type the softener is unavailable during the regenerate process, which can take a couple of hours - so any water used at this time will be hard. Normally regeneration is timed to take place at a time when you won't be using water ie, in the night for most people. All sorts of cunning methods are used to sort out how often this is, from a simple timer (you set it to regenerate say every 3 days) to a computer system which measures your usage and tries to predict when you are going to need a regeneration and sets it off the night before. It can, of course, get it wrong if, say, you go away for a few days and then come back with several loads of washing and a dirty car. To get around the problem you can force a regeneration if you know you have high-usage coming up.
The twin-cylinder machines have two smaller cylinders and use only one at a time. When one cylinder needs regenerating it flips to using the other one and regenerates the first. That way you never run out of soft water and salt-usage is minimised.
Each system has its advantages - the single-cylinder machines are cheaper but need a mains electricity connection for the timer. The twin-cylinder models are more expensive, do not need electricity (as the mechanism is powered by the water-flow), use less salt and never let your water go hard. The snag with the water going hard whilst you're using it is that it gets into the hot-water cylinder and takes days to get fully soft again.
Salt is relatively cheap, so I wouldn't put too much weight on how much the savings will be with one type against the other but the convenience of knowing that the water will never run hard is worth thinking about.
We've had both types and I would have no hesitation in recommending the twin-cylinder type; other people will have different recommendations.
Finally, to answer your question, we got our last one from a company called East Midlands Water, as did our daughter several years before us. We found them on the internet (so not local to us in Reading), their price was good and they were happy to give us advice via email.
I would further add that if you are fairly competent at plumbing fitting them yourself is easy. Because we wanted ALL the water in the house to be soft, including the drinking water, we removed a short length of pipe straight after the main stopcock and replaced it with T-piece, stop valve, T-piece. Pipe from the first T-piece to a washing-machine stop tap and pipe from the second T-piece to a washing machine stop tap. The pipes to the softener are similar to washing machine pipes so can be connected to the stop taps. By turning on or off the 3 new stop taps you can isolate the softener, should you need to remove it.
A final requirement is a drain pipe for when the softener regenerates. This is like the drain pipe from a washing machine and can be connected to a suitable plastic drain eg, sink using easily-available kit.