The version I know from Lincolnshire is similar to Joe's but with a shorter refrain;-

Oats and beans and barley grows
As you and I and everyone knows
For oats and beans and barley grows
As you and I and everyone knows
Waiting for a partner

First the farmer sows the seed
Then He stands and takes his ease
Stamps his foot and claps his hand
And turns around to view the land
Waiting for a partner

Do you want a partner?
Do you want a partner?
For if you do, you must be true
And choose him very shortly
Waiting for a partner

Now you're married, you must obey
You must be true to all you say
You must be kind, you must be good
And help your wife to chop the wood.
Waiting for a partner

In the local accent (if you ever see Brian Dawson he does it brilliantly, or used to anyway) the first line becomes

Whuts and bee-yans and barley grow-us

Likewise 'partner' is sung 'par-ten-er' which also helps it scan to the tune.

all the best

oggie