Sash window rattles and lets in a draught but the cords still work fine Windows & Doors

Cheapest first, and in this order:

1. Fit a proper sash fastener that pulls the two sashes together rather than just holding them closed. A Brighton fastener or a screw-down fitch catch does this — it forces the meeting rails tight against each other and cures both the rattle and most of the draught in one go. Under £20 and half an hour.
2. Brush pile draught strips in routed grooves along the staff beads and parting beads. This is the proper job and it's what specialist sash companies charge hundreds for, but the strips themselves are cheap and you can do it with a router or even carefully by hand.
3. Only after those, consider secondary glazing or heavy curtains for the remaining heat loss.

The rattle specifically is nearly always the fastener, not the beading. People go straight to draught strips and are then annoyed it still rattles.

Worth checking where the draught actually comes from before you spend anything. A stick of incense or a lit match held near the joints on a windy day will show you — often a good chunk is coming through the box behind the frame rather than at the meeting rail, and that's a different fix.

Check the parting bead too. On a window that's been painted a dozen times the bead often gets loose or has been replaced with something too thin, which lets the upper sash move front to back. You can pull it out and shim it or replace it for a few pounds a metre.

Good instinct not replacing it. A sound 1890s sash with working cords is better joinery than anything at a comparable price today, and repaired properly it'll outlast a replacement unit by decades.

Careful with the self-adhesive foam tape approach, which is what most people try first. It works for one winter, then the adhesive fails, the sash sticks to it in summer, and you're picking gunge off the beading. Brush pile in a groove lasts decades.