Sought out this thread because I recognised the tune on the recent programme on the first part of 'The People's Post' on Radio 4 on Friday

http://www.bbc.co.uk/programmes/b017x7g8

- two more parts to come, I think on 16th and 23rd Dec. The programme was using the 'open the door and let me in' verse and it was the instrumental part of the song which I recognised from Edinburgh in the 1960s as 'one, two three a-leerie' (that was the spelling I assumed was used, never having seen it written) finishing 'ten a-leerie , Postman', as mentioned earlier.