What is it called: A plant that produces...

[KARL]

.... berry that looks somewhat like a raspberry but has smaller individual components and is bright red (even very slightly on the orange side) rather than wine coloured ? The berries have a very nice flavour, more tart than the raspberry but not as tart as a blackberry. The leaves look more like those of a currant than those of the raspberry bush and the stems bristle with thorns that are softer than those of the bramble. This plant seems initially to grow quite low and ground-hugging but then gets bolder and higher.

[Clanad]

Nearly all of the attributes you describe in your plant can be replicated in various cultivars of Rubus. A number of raspberries here in the U.S. are different in color, texture and growing habits than the usual, how do you say... bog standard raspberry. One we grow imported from Britsh columbia, Canada is the Anne and is nearly yellow with orange tints and grows much clsoer to the ground than the cane variety. (You do know that the berry is closely related to the Rose, no?)
If your berries matured into darker colors, here in the U.S. I would suspect a Boysenberry...