From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
The green fibers pattern will work very well in grayscale as well.
Source Matteo Di Capua
Light and tiny, just the way you like it.
Source Rohit Arun Rao
A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
A good starting point for a cardboard pattern. This would work well in a variety of colors.
Source Atle Mo
Not the most creative name, but it’s a good all-purpose light background.
Source Dmitry
To get the tile this is formed from select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Cowdray: the history of a great English House', Julia Roundell, 1884.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
Prismatic Geometric Pattern Background 2 No Black
Source GDJ
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin