A misgiving title perhaps, as these two flies are most certainly found in a variety of flowing water other than chalkstreams; but if you frequent this type of environment they will feature highly in the diet of the trout.
Shrimp patterns vary greatly - from simply dubbed bodies with a shell back, to more realistic ties incorporating various appendages and an overall more close-copy look.
I tend to sit in the area occupied by the more realistic flies and although it may seem tricky to tie, Oliver Edwards shrimp is by far one of the best out there.
Ephemera danica - the mayfly - needs no introduction. My mainstay dry mayfly pattern has always been the Mohican mayfly; you may spot a common trend, I do love Oliver Edwards patterns, I have no shame in using a lot of his flies, but I digress.
Although the Mohican mayfly is an outstanding fly, sometimes it makes a change to try something different. Having received a copy of Peter Hayes' Fishing outside the box, he wrote that he uses slightly larger PhD's for fishing early in the mayfly hatch when the trout haven't yet got over the size of the real things. Taking things a little further, a PhD tied to represent the mayfly seems logical. A pack of Nature's Spirit mallard flank dyed light olive proved to be a great match for the yellow-olive wings of the natural dun.