No, in the UK (& most of Europe?) instructors will generally have a CPL or ATPL, as we need a professional licence to allow us to be paid. Although under the JAA rules you could get an FI rating with a PPL, but not be paid, this option required the applicant to have more PIC time and to have CPL TK. So it wasn't a particularly popular option, I personally only know of one person who did it that way. As we change over to the new EASA regulations, they will allow the PPL holder with FI rating to be remunerated and to instruct for the new LAPL, they won't need CPL TK, so we may see a this being a bit more popular.
There's no requirement at all, to have any instrument qualification to teach the PPL.