Cameron was clear in the Referendum that this was a one-off decision, that if there was a vote to leave then that meant the UK was leaving. He didn’t promise that he would immediately activate Article 50 but I think there was an assumption that that’s what he would do. He told the House of Commons in February 2016 that “the British people would rightly expect [triggering Article 50] to start straight away” in the event of a Leave vote.
https://www.youtube.com/embed/Hex78gJebOo?wmode=opaque
However, there was always going to be a degree of vagueness. The legislation that set up the Referendum didn’t say that the result would bind Parliament or be taken as a notification [trigger] of Article 50, and we still don’t have clarity on how Article 50 works itself or how it works within UK constitutional practice.
"If you don’t know what you want, it’s very hard to get what you want"
There’s a secondary point here, too, that because there hadn’t been any forward planning for a vote to leave there wasn’t – and there isn’t – clarity about what relationship the UK wants with the EU. The reason that’s important is that Article 50 doesn’t put much power in the hands of the UK. It’s the 27 member states of the EU who offer the UK the form of the relationship and that’s then accepted or not by the UK. So it makes sense to hand in your notification of Article 50 together with a declaration of your aims in the process. If you don’t know what you want, it’s very hard to get what you want.