Woodward would make me think it was English made possibly. Believe it or not, I have the EXACT SAME PROBLEM as you do...
Nobody can tell me what this thing is either. It looks to be a late 70's to early 70's 20" folding trike (based on mere deductions)... and thats where I get stumped. 3 piece cranks, like yours, and the handle bars and front forks are wrong so as far as I guessed was a Worksman (?) or a Kent (???). At least you got a name to work with. I've almost given up myself, but keeping my eyes open to see anything to comppare it to.
Good Luck!