i am a ground worker/block paver and we often use weed killer before and after completing a job.
the absolute best weed killer is sodium chlorate. it kills everything, including grass, so you have to be carefull using it.
next is pathclear.
do not cut plants, spray or paint on pathclear to the leaves and the weedkiller works its way down to the roots. this usually takes around 2 weeks.
the more leaves you spray, the better
also you need to give your patio a good cleaning. hire a jet wash and give it a good clean.
then when dry, buy some kiln dried sand from b&q or wickes and brush sand over it.
you can also buy a resin (like a clear varnish) to paint over the blocks, this will also stop the moss and weeds from growing back.
the best one is resiblock superior