To my knowledge there is no complete British set of hones.
UK stones tend to be available from about 4-5K to 15K+. Lower than 4K there isn't anything that was used historically.
The old method to begin to sharpen was to file or sand sharpen the edge, Then work with a finer grit stone until you had a fully set edge. It's why there was a massive demand for the Arkansas stones when they became available, Since they have bevel setters all the way up to finishing stones. Steel is far harder than iron as well so stones that were used for say Viking or roman blades tend to be very slow on steel.
If I were to pick a stone to work on all those blade types then it would be an impossible task. They all have different needs.
The scythe and sickle should be set with a nice Carborundum oval whetstone. There cheap as chips on ebay.
The fishing knife, and chisel can also use the same stones, Finishing at about 2-4K grit.
The razor needs to go much higher 8K at the lowest.
The push mower I would probably use a long file on, The bed knife doesn't need to be perfect just straight with a reasonable edge, A bit more meat on that edge will stop stone damage. So perhaps a single underside bevel and leave the top flat so it sits well on the blade. The cutting action for those mowers is 3 fold. You have the edge cutting of the bed knife, The distance between the bed knife and the blade to snip, and the angle of the blade to provide shear against the bed knife. In most mowers I have looked at the bed knife while blunt still works, but a damaged blade gives far more problems.
If your dead set on UK based stones then your only option is vintage. I know of no UK manufacturers producing stone today for sharpening.
If you want a full natural set out of the ground then the only option is Arkansas stone. It's the only complete natural stone set. It's from the USA, but rest assured it was the stone of choice ever since it was discovered right until it was replaced with carborundum.
Dans whetstones has a full selection of grades and how those grades work.
Arkansas sharpening stones, flintknapping, sandstone coasters, knife sharpening
The 8x1x1/4 4 stone set here would be fine for most of your needs, There a little narrow for razors, and may suffer from ovaling on the scythes tho.
EZ Hones
If your dead set on UK only stones then I would look at the 3 slate pack on ebay. It's not very well regarded for razors, and is slow to remove metal.
For a uk razor finisher you have more options, Charnley forest, LI, Tam o shanter, Dalmore blue ect. The highest regarded stones still fall out of UK waters. A nice all rounder would be Belgian Coticule. It's located not far over the pond and can be used from bevel set to finish if you put the effort into learning the stone.
http://www.ardennes-coticule.be/en/