No 8-bit computer (back then) supported proportional fonts out of the box, but there where some programs on almost every bitmap-capable 8 bit computer. I this would include the Spectrum.
For the Apple II, support was added by Apple rather early. Already the Apple DOS Toolkit included a utility called HRCG or High Resolution Character Generator, which moved character drawing onto high-res bitmaps and into software (*1). While, AFAIR, it originally only supported fixed-width fonts, soon other programs used this to display at least part of their output in proportional-width.
When the Apple II Mouse was introduced, first for the IIc and later the basic II, it came with MousePaint, a MacPaint clone for the Apple II using proportional text on screen and in menus (*2). The availability of a mouse also triggered a lot of other programs trying to do what the Mac showed on an Apple II. Most notably maybe MultiScribe for the II (*3) and MouseDesk.
Another example for add-on software enabling proportional fonts would be DR's GSX, the graphic extension (*4) for CP/M, which was also adapted to several Z80 machines including the Amstrad CPC and Commodore 128. It was also the core component for GEM on the Atari ST and PC.
And then there was GEOS. It enabled C64 programs to use proportional text and exchangeable fonts. Soon also ported to the Apple II.
So, bottom line: No, it hasn't been used out of the box, but later tools added this capability to 8-bit computers.
*1 – It was slow (compared to text mode) and it ate up memory, but it was also AWESOME.
*2 – Not to be confused with MouseText, a character set change for the Apple IIc and Enhanced IIe introducing some graphic elements into the character set, allowing character-based software to display a simplified GUI. Funnily enough, soon programs used HRCG with Mousetext to draw the same elements using the graphics characters, but also add other graphic elements.
*3 – Which got a second life as BeagleWrite after their company was bought by Apple and integrated into Claris.
*4 - It was much more than just an average graphics library. Beside being made to the GKS standard, it also includes features for multiprogramming and windowing.