I'm a sucker for the neatness of the square.

That looks like it. Some call it crazy paving. It usually gets laid over compacted paving sand/s. The joins between each flagstone are usually concrete with the edges concreted so it stays in place. I have seen some with sand between the joins which also looks good. New sandstone from Gosford Quarries looks superb but is expensive. (its a great product!). I'd look for some second hand stuff on Ebay/Gumtree/etc.

there are way too many colours going on here. Your home is a traditional style and yes the cream and green are traditional colours with the reddish brick however why did you put grey around the windows??also you have red scollops above the grey and it doesn't do the house justice. What colour was there before you painted the grey?? considering grey is a more modern colour I think you were attempting to modernise the externals. in saying that the roof would have been better to paint charcoal the cream in white and then the grey and then the driveway would be done in a grey stain. but if you leave it the way it is and cover the red scolloping above the windows the same grey and the bricks below the windows near the ground grey as well then get the drive way restained to the reddish colour of the bricks on the house and then it would blend more and look inviting.

Hi JE C, You could try baking soda, mix with water and a little detergent, treat area leave about 30 minutes then give a bit of a scrub with broom and rinse off, I use this to remove marks off brick paving, always have baking soda on hand it works amazingly for so many things.