Cleaning york stone paths, terraces, steps and patios is a chore but a necessary and easy one which can reward the effort.
There are, I think several important points to remember, particularly with reclaimed yorkstone paving, it is the patina on the surface that distinguishes it from freshly quarried stone and which commands a small cost premium, so aggressive, abrasive cleaning should be avoided simply because it will remove that patina. Both reclaimed and newly quarried yorkstone are the same age, formed in the same geological periods, reclaimed looked like freshly quarried stone when it was freshly quarried.
York stone is a porous material, lots of very small particles glued together with minute pores, whilst in the ground the pores are full of liquid ( nature abhors a vacuum) that liquid will hold in suspension and solution minerals associated with the stone. After quarrying as the moisture evaporates those minerals are deposited on and just under the surface and start to oxidise, changing the appearance of the stone, this, and the polishing effect of wear is the process that causes the difference between newly quarried and reclaimed yorkstone, therefore if you remove the weathered surface the exposed substrate will not be as mineral rich as the surface removed and will almost certainly never look the same again.
This is why I recommend avoiding all aggressive, abrasive cleaning and particularly the use of chemicals, because the stone is porous it will absorb the chemicals and you will not be able to remove them. I include, soap, soda, bleach, detergent and acidic cleaners in this category as well as fungicides and selective herbicides.
Pressure washers in my view simply don't do a very good job they leave the paving unevenly cleaned making it look "streaky" and in my judgement are so abrasive it most probably will cause uneven erosion and even delamination.
So far I've been writing about what shouldn't be done to clean yorkstone paving.
So, what should be done to clean your yorkstone, nothing? that is often the best answer. But, not always, depending on where the stone is the likelihood of algae and other organisms that flourish in situations that vary between damp and dry and cold and warm, in fact just about everywhere outdoors is pretty much inevitable, and they can be a little slippery. Elbow grease is still by far the most effective, safest and most environmentally beneficial cleaning agent known to man, especially when enthusiastically applied with a very stiff yard brush and water, occasionally a little soil or possibly even sand on areas which provide the kindest growing conditions for algae usually damp shaded corners and areas of paving that are subject to pooling.
So as spring approaches and everything warms up, out with the scrubbing brush!