Sindy
 
Simply put, Sindy was the fashion doll of the UK, beginning in the early sixties through to today.  She was significantly cuter and more wholesome (or frumpy, depending on your view) than Barbie, but basically filled the same niche- a fashion doll with hair to style, supplementary outfits, playsets & furniture, etc.  By the mid '80's, she began to appear with several Jem-like traits, such as pink hair and iridescent jump suits; by 1987, Hasbro had bought out Pedigree and with it Sindy's look changed radically.  It was at this point that many suspiciously Jem-like objects began to appear in the Sindy line. 
For the most part, Sindy was a UK phenomenon, though she was available in Canada and the US (at least, probably elsewhere) at various points in her history. 

Please go to Elizabeth's Sindy Doll Fan Page and My Sindy.com for a much more in depth history of Sindy!

All photos shown here are courtesy of Gina.  Thanks!
Year A Brief Chronology (Jem-like occurences throughout the Sindy line, as far as I know of!)
1985 Space Fantasy Sindy- A pink haired, metallic-fabric-wearing alien doll!
1985, 1986 Starlight Sindy, wearing green or red iridescent jumpsuits (fabric is reminiscient of Video's jacket).
1986 Colour Magic Sindy: with a new face, and hair that turned from brown to blue when wet. 
1986 Disco Magic Sindy.  I'm not sure if they were all sold separately or only on dolls or both. 

Bafflingly, the bottom four fashions (with Barbie sized shoes) were released in the US by a different toy company -Creata- for the Rocker knock off doll, "Lace." 
1987 Sindy is bought out by Hasbro.  After 20+ years, the dolls are no longer made by Pedigree.
1988 Where the fun begins!  Superstar Sindy debuts.  Looking rather more Barbie and the Rockers-ish to me, but appears to be wearing Jem bracelets, and holding a Jem microphone. Note the tinsel in her hair too!
1988 The Superstar Fashions - probably the most exciting to Jem fans.  Please note I have not seen these fashions in person and I'm only making guesses based on the photos!
 
  • Fizzy Pink: Shown here as a pantsuit, in the 1989 catalogue the bottom half of the fashion is replaced by a miniskirt made of 2nd edition Aja's skirt fabric.  Both fashions come with what appears to be the same microphone that was issued with Glitter 'N Gold Jem.  The bracelets also look like Jem's.

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  • Golden Light: The vest here is apparently the same as the one from 24 Carat Sound, minus the hoodie.  It also came with the same microphone and bracelet that was issued with Glitter 'N Gold Jem.

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  • Crimson Pearl: Appears to have come with the same microphone and bracelet that was issued with Glitter 'N Gold Jem.

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  • Blue Haze: A minidress made of the material from the Moroccan Magic dress, in the 1988 catalogue photo (right) or Video's jacket (in the 1989 catalogue,).  The socks look like similar to those from 24 Carat Sound.  Also appears to have come with the same microphone and bracelet that was issued with Glitter 'N Gold Jem, possible other bracelets as well.

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    1988 Fashion Mixers 1 & 2,  Fashion Mixers 3.  Not particularly Jem looking to me, but still interesting in light of the Matchin' Medley's concept for Jem '88, that never got off the ground. 
    1988 City Girl Fashions.  Again, not particularly Jem-ish, but as the prototype stuff from Jem 88 pops up, maybe we will find something...
    1989 Super Star Sindy must have done wll, she is reissued in 1989, with what looks to be a new face mold.  That top looks a little like the one from 24 Carat Sound to me, I wonder if it's the same fabric?
    1989 Disco Mixers, The Superstar Fashions are re-issued, with a few changes in the materials (explained above) 
    1990 Smash Hits Sindy: The pop star doll theme is still running strong, though there no longer appears to be any obvious tie to Jem anymore. 
    1990 Smash Hits fashions. 
    1991 Hot Blades Sindy is issued with a Jem shaped comb, not that you can tell from this photo. (Thanks to Debbie for pointing this out!)  Club-Sindy has a good picture of it.  
    1993 Wild Hair Sindy: Comes with hot orange lightning bolt earrings.  Not really a Jem tie-in, but pretty cool!