I don't think so. As far as I know they only made the SS80 & SS100 + varients which,I think, used JAP or Matchless Sidevalve V twins. They did make a 4 cylinder ( Austin 7 Engined?) twin rear wheel bike but I think that was just for shows, I don't think it was ever commercially available. Nice if you're Grannies got one in her garage, prices for a rusty heap start at £40K up to £100K for a minter!!!.....I wish...
If you want something REALLY rare I think I've found it. Even rarer than you're Icky GC! ( 2 in the country and only one running)...I'll post some photos later and see if anyone knows what it is. It's not mine by the way, I spotted it at a local Classic show.