Q:

Use of the term "reckon"

Did the use of the term I reckon originate in the UK or in the southern US?  I hear the term being used both in British English (like on the BBC) as well as in southern US dialect.

A:

It is not possible to be completely certain what you are asking, because the verb reckon can be used in many ways, all of them with a subject in the first person singular. It looks to me that this wasn’t something you reckoned with, unfortunately.
But the one you’re thinking of, I imagine, is the one that could replace the first instance of imagine in this sentence.  The OED says that this is used parenthetically or finally, and that

Formerly in literary Eng. use; still common in Eng. dialects, and current in the southern States of America in place of the northern I guess.

So it certainly began in England where it saw literary use, and is still common there in various dialects as well as a distinctively Dixie thing in the States.
The first citation for this sense antedates Plymouth Rock:

1603 Sir R. Cecil in Harington Nugæ Ant. (1804) I. 345 ― He is, I reckon, no wise man that looketh this waye to heaven.

However, it is also possible that you’re thinking of this very slightly more general sense:

To consider, think, suppose, be of opinion, etc., that. Also with omission of that. Now usu. colloq., esp. in the U.S. (formerly chiefly in southern States).

The first citation is from the early 1500s, and two centuries after that Jonathan Swift was using it in the modern way when in 1712 he wrote:

I reckon the Queen will go to Windsor in three or four weeks: and if the Secretary takes a house there, I shall be sometimes with him.

Here are two recent citations of the same use:

1963 Social Problems Spring 367/1, ― I reckon it’ll always be lucky.

1977 I. Shaw Beggarman, Thief ɪɪɪ. ii. 193, ― I don’t reckon I’ve had a fare there for more than ten years.

Perhaps these are not the senses you were looking for, but if you would be so kind as to elaborate your intended sense, you can reckon on further OED citations for that one, too.

