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
Not a flat you live inside, like in the UK – but a flat piece of cardboard.
Source Appleshadow
A bit like some carbon, or knitted netting if you will.
Source Anna Litvinuk
Remixed from a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Bright Multicolored Floral Background by Karen Arnold from PDP.
Source GDJ
This was formed by distorting an image of a background on Pixabay.
Source Firkin
A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.
Source Josh Green
From a drawing in 'In an Enchanted Island', William Mallock, 1892.
Source Firkin
Semi-light fabric pattern made out of random pixels in shades of gray.
Source Atle Mo
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Prismatic Floral Pattern 3 Variation 3 No Background
Source GDJ
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Remixed from a drawing in 'Line and form", Walter Crane, 1914.
Source Firkin
Prismatic Abstract Line Art Pattern Background
Source GDJ
Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.
Source Firkin
Tile-able Dark Brown Wood Background. Feel free to use it as a background image in your designs or somewhere on the web. By the way, the color seems to be close to Coffee Brown.
Source V. Hartikainen
More in the paper realm, this time with fibers.
Source Jorge Fuentes
Zero CC tileable Laminate wood texture, photographed and made by me. CC0
Source Sojan Janso
In the spirit of WWDC 2011, here is a dark iOS inspired linen pattern.
Source Atle Mo
Background Wall, Art Abstract, Block Well & CC0 texture.
Source Ractapopulous
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
Remixed from a drawing in 'The March of Loyalty', Letitia MacClintock, 1884.
Source Firkin