A fairly cheap way of alleviating the noise problem is to pad the space between the joists with Rockwool insulation, which can be bought from places like Wickes.
This will not stop all the noise because the joists will meet the floorboards.
You will have to be sure that the ceiling can support the weight.
Good quality underlay and thick carpeting will also help.
In my house, however, the noise seems to travel up through the cavity walls.
Cork of course is excellent soundproofing. Cork tiles are cheap, warm but ugly. It could be worth trying this with additional flooring covering on top.
Good luck with it.