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
The act or state of corrugating or of being corrugated, a wrinkle; fold; furrow; ridge.
Source Anna Litvinuk
Prismatic Groovy Concentric Background 4 No Black
Source GDJ
A free seamless background image with a texture of dark red "canvas". It should look very nice on web sites.
Source V. Hartikainen
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
A light gray background pattern with seamless fabric-like texture and almost unnoticeable stripes.
Source V. Hartikainen
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
I love these crisp, tiny, super subtle patterns.
Source Badhon Ebrahim
Tiny, tiny 3D cubes. Reminds me of the good old pattern from k10k.
Source Etienne Rallion
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Never out of fashion and so much hotter than the 45º everyone knows, here is a sweet 60º line pattern.
Source Atle Mo
I guess this one is inspired by an office. A dark office.
Source Andrés Rigo.
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
As far as fabric patterns goes, this is quite crisp.
Source Heliodor Jalba
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A bit like some carbon, or knitted netting if you will.
Source Anna Litvinuk
Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Detailed but still subtle and quite original. Lovely gray shades.
Source Kim Ruddock
From a drawing in 'Studies for Stories', Jean Ingelow, 1864.
Source Firkin
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A brown seamless wood texture in a form of stripe pattern. The result has turned out pretty well, in my opinion.
Source V. Hartikainen