These fabrics were loomed on narrow home looms, widths vary but are rarely greater than 60cm a panel. Cart covers, sheets, mattress covers have all been made by sewing panels together, they are often beautifully hand sewn with hemp thread.
Cart covers are ideal for larger pieces and easier than fabrics from roll because the lengths are already hand sewn together.
These two pieces by Dan Marty design, the sofa is covered using what looks like a cart cover

The patchwork effect is also popular and often uses a mixture of grain sacks, of different colours with varying stripes and the odd monogram thrown in. This one is from Antiquted

and this one here from Hossack and Gray, this sofa is upholstered in a ix of striped and hand dyed vintage fabrics

and here is one, also from Hossack and Gray upholstered with indigo dyed vintage linen