Seeking 'The Policeman'

My 'junior' school (from age 7 to age 10) education included weekly poetry lessons, hosted by the Headmaster. The poetry handbooks would be distributed around the class to each pupil. Next, the Headmaster would set up an old record player on the teacher's desk, and play records containing the spoken versions of the poems, whilst we followed the text within the poetry handbooks.

At the end of each term, the Headmaster would hold a poetry competition, whereby you would try to memorise the poems and recite them word for word. You would get a point for each line recited correctly, until you got a line wrong, and then you were out of the competition. You only had the time whilst other people were reciting to memorise the next poem. The person who recited the most lines without error was the winner. The winning pupil would receive a book token during the afternoon Assembly on the last day of that term. Fortunately, I won the prize every term and every year I was there, and those book tokens helped to furnish my collection of Spike Milligan books, the first two of which were poetry books ('Silly Verse For Kids' and 'A Book Of Milliganimals').

Anyhow, in my first year (and my first term), one of the poems that helped me win was entitled 'The Policeman'. I don't know who wrote it, and to this day I can only remember the second and third verses. They are as follows:

As he holds up his hand,
All the traffic has to hand.
Every car, every bus
Has to stop without fuss.
They must wait in a row
'Til the policeman tells them: 'Go!'
They must wait 'til the policeman tells them: 'Go!'

And if anyone's about
Who shouldn't be about
Then there isn't any doubt
That they should very soon look out
For the tramp of the feet
Of the policeman on his beat
For the tramp of his feet on the beat.

If anyone recognises this poem, I would be grateful to learn the name of the author, and more importantly, the missing first verse!