Not a major project, but very fiddly on your own and one that requires a little touching up afterwards.
The sliding windows are held in place by parting beads, with a stop bead at the front. These beads will need to be removed, together with the windows, to get at the small access panels to the side of them. Behind this panel are the weights and cords.
Sash window cross section
Use a sharp chisel and prise off the outer stop bead. It is sometimes an idea to run along the joint with a Stanley knife before you start with the chisel. This will sometimes save chips of paint coming off.
When both stop beads are off, the inner sash can be lifted out of the frame. Be careful they are heavy. If it is this sash that the cord is broken on then you can probably leave the top in place. If not, prise out the parting bead with the chisel and this will free the top sash.
Whichever sash you need to work on the weights will be behind the weight cover, which you will need to remove. This should just pull out.
Locate the broken cord and remove the nails that secure it to the groove in the side of the sash after pulling its weight through the weight box.
Take a length of new cord (these can be bought at builders merchants in rolls, try and get the waxed variety) and feed it over the pulley that the old one served. This may be more easily done by tying a piece of string to it first, then feed that over the pulley until you can reach it and pull it through. Then untie the string but secure the end of the cord first so it does not disappear. The cord should be fed from the window side, into the boxing and down to the weight box.
Now tie the weight to the cord as you can see the old one has been done.
For a top sash, put the side of the sash that has the existing cord, back onto its side of the frame, and make sure that the bottom of the sash is about 4 inches above the cill. Then pull the new cord so the weight disappears into the box and keep pulling until you hear it hit the top of the box. Then you must nail the cord, with the weight in this position. Nail exactly as the other cords are nailed, no higher or lower in the groove. Use the same tie off knot if there is one. Now you can replace the sash and as you push it up, the new weight will fall.
For the inside sash the procedure is the same, make sure the sash weight is at the top of the box when the window is at the bottom.
Fix the centre-parting bead, replace the bottom sash and fix the stop bead.
Should you break any of the timber mouldings, you will probably find that a local joiners shop will stock them.