Hi, Linda,
It's a question of balance. The hot water naturally wants to rise to the upper radiators, as hot water is lighter and 'floats' to the top of the system. By closing the valves upstairs the flow is only to the downstairs radiators as they are now the top. You will notice however that the pipe to the valves upstairs should be hot below the valves.
What you have to do is go to the valve on the other side of the upstairs radiators and reduce the flow, close them down a bit but not completely. There is usually a plastic cap to pull off and there is a screw inside, turn this clockwise to close and anticlockwise to open. In addition you can 'open' these valves a little more on the downstairs one to increase the flow, but they should be almost fully open anyway.
You may have to do a bit of running around, but keep checking on it and adjust if necessary. You can even do it over a few days to get the balance just right. It is also worthwhile getting a radiator 'key' from your local DIY and bleeding out the air on the topside of each radiator. You just open slightly until the water comes out, then close. Hope that is clear.
Malcolm X, October 2007