Apparently, in this particular case, Ed Vaizey voted against the amendment by mistake. Then he had to vote the second time to nullify his vote.
Today, Vaizey retweeted his constituent praising him on supporting the amendment, which, in a way, confirms that he originally intended to vote "aye" and voted "no" by mistake:
Good to hear that my MP @edvaizey was one of the Tory rebels who supported the Letwin Amendment yesterday. Common sense is starting to prevail.
@theoelliott 5:20 PM - 26 Mar 2019
In another tweet, Vaizey confirms the Mirror report that he voted by accident the first time:
I can now look British Airways pilots in the eye
@ch33sl3y Replying to @June4th
"NOTE: A 30th Tory, Ed Vaizey, voted both aye and no. Normally this is known as a 'positive abstention' - but the Mirror understands he voted both ways by accident!"
You couldn't make it up.
@edvaizey 11:07 PM - 26 Mar 2019
Here, Vaizey compares himself to the pilots of British Airways who recently landed in Scotland instead of Germany by mistake.
MPs are not allowed to change their vote, so quickly voting again is the only way to cancel a vote by error (Division factsheet from the House of Commons Information Office):
There is no means in the House whereby a Member may register an abstention. But Members
may continue to occupy their seats during a division to signify abstention.
A Member who has voted by error may, if he or she has time, cross over to the other lobby and vote again, hence nullifying the effect of his or her original vote, though of course this procedure does not allow him actually to register a vote in favour of the proposition on which he made the first mistake. Members can also, if they wish, stay in the lobby and not register a vote at all.
Also, an MP can vote both ways deliberately to signal an active abstention.
Public Whip has a list of 726 occasions of double voting.
Amazingly, on 726 occasions in these parliaments, an MP has voted twice in the same division. It's a little known fact that this is perfectly allowable, provided one vote is aye and the other is no. For details see under the heading "abstention" in the division factsheet from the House of Commons Information Office.
An MP may have done this to cancel the effect of a mistaken vote in the wrong lobby. However, it would seem reasonable to encourage the practice as a signal of active abstention from the vote. You can see in the table below one clear case of this happening, where many Conservative members abstain on a fishing issue.