One approach would be to use coving. If that's not an option first of all paint the ceiling ( 2 Coats of best quality paint)
It doesn't matter if the walls are smudged or overcut as long as the ceiling paint goes in 'solid' ( Use Matt emulsion)
Next, stir the darker emulsion, decant a small amount to a paint kettle (buy them in Wilkinson's - plastic will do) and choose a good quality paintbrush which should be at least 2.5 inches wide if not more.
Get your steps into position when the ceiling has dried out and practice using the brush without any paint on it first of all. Decide which hand is going to do the painting, the brush should be roughly at a 45 degree angle between wall and ceiling.
When you feel comfortable load your brush with emulsion from the kettle, wipe off any excess one one side of the paint kettle.
Start away from the corners and rest your hand so that you paint a steady line with the edge of the bristles, cutting in to the white ceiling.
Continue cutting in along your line painting up to the finished surface (the white ceiling)
It doesn't matter if paint goes onto your hand, it will wash off and dont worry too much if you stray over your chosen line because you can always dab a bit of white emulsion on later to cover any mistakes.
Take your time, work up to corners using the end bristles and you should achieve satisfactory results.
If all of this fails - get a painter!