Until they catch somebody who's been through one of these gates and say "prove how you came in to the country". You have no access to the UK Borders Agency systems or the airline systems and even if you had kept your boarding card, that is only evidence that you checked in for a particular flight (it could trivially be alleged, for example, that you merely changed flights at Heathrow - therefore never actually entered the country.) But, still, from the explanatory note:
where any question arises under the Immigration Acts as to whether a person has leave to enter the United Kingdom and the person alleges that the person has such leave by virtue of passing through an automated gate under article 8A, the onus shall be on the person to show the manner and date of entry into the United Kingdom.
I'll note that in the other cases from the 2000 SI, as originally implemented, you were either given leave to remain by telephone or by a notice to a responsible 3rd party. In both these cases, I would assume that you would have had some documentation of your initial entry to the UK in your passport - which is what you have to prove - when and how did you enter the UK. It is the "leave to remain", subsequently granted and which you are not required to prove, that comes without a document.
Bastards. Just evil bastards. I'll note that this cunting thing is a draft - I hope, but strongly doubt, that they'll fix it.