It doesn't look like a HQ headtube sticker to me and the serial number in the BB isn't a HQ number. I read on a page I found through Google, in the 80's that some cheapo Japanese frames were sold under the HQ name? (Might explain the Sakae BB and Tange headset!).
I am really interested to find out a bit more about this frame so if you can help give me a shout!
I don't think its a Harry Quinn. As far as I know all Quinns had a decal for the headbadge but your tube looks to have been drilled for a rivet fitted headbadge. Not a lot of help but I think it rules out Harry Quinn.
Ernie Clements bought Harry out at one point and imported cheapo frames which he rebranded as Harry Quinns. He owned the company so he held the rights to use Harry's name. These frame don't have the 'Q' prefix to the frame number. I think these later frames still used a decal for the headbadge though.