Flights booked and tickets issued but no charge on my bank account?

Update: thanks for the replies! I did phone Expedia yesterday and after two hours on the phone the woman told me she would ring the airline, she told me to hang up and that she would call me back or send an email confirmation. After waiting all day and cancelling plans she never got back to me! I contacted Expedia again today and they kept insisting I had paid, no matter how many times I explained the situation their reply was the same, (it was like repeatedly walking into a brick wall) they didn’t believe me and it made me feel like an idiot! Why would I insist they take £500 from me if I’d already paid?! Anyway, the woman finally agreed to call the airline on my behalf, an hour later I was connected through to the airline support team and as far as they were concerned it was paid for. However they did offer to place the payment under investigation, so now I’ve just to wait for them to call me back in a few days hopefully all sorted. Prior to the call, I did consider cancelling the flight and rebooking directly with the airline but the price has risen at least £200 and I’ve already paid significantly extra for baggage and seats. Also I didn’t want them to charge me in the future and not be a bale to receive a refund. At least I know never to use Expedia again!

That is one of the problems of booking with a consolidator.

If you have the airline booking code (6 characters), you can log on to the airline and see the booking there. Alternatively, many airlines allow you to search for the ticket number, and verify the ticket is issued. That is normally trustworthy - normally. But it could still go wrong, and you show up and they say the ticket was cancelled. There is no good solution.
I had a similar situation, and ended up having to buy two new tickets at the gate, for each about 14 times the original price (not going was not an option). It turned out later that the consolidator had cancelled the ticket because the flight was moved 5 minutes, so the airline refunded them, and I got informed later by them that I have now a credit with the consolidator for that amount (thank you very much...). However, even up to a month after the flight, the consolidator showed the ticket as 'valid and confirmed'. Lesson: Consolidators bring a huge risk for the small amount you save when booking through them instead of directly with the airline.

I don't think anyone can for sure say how your situation will end.
My recommendation - if you want to fly - bite the bullet and buy another ticket directly from an airline now while they are still relatively cheap. Yes, you will lose the first ticket if they charge you after all, and yes, you'll pay more than originally, but it could be worse. A lot worse.

I'm not too familiar with the airline industry, but the way this works in the hotel world (which is probably pretty similar), when you book the Online Travel Agency (OTA) sends a message to the hotel's system which says "Hey, someone booked a stay, here are the details of the stay, and here's their payment data". The hotel's system is then responsible for actually charging the card (when you check in, when you no-show, or at whatever other time their policies say).

As far as Expedia (the OTA) is concerned, if the hotel's system responds with an "Ok, I've got it", then they can tell you that it was booked, mark it as such in their system, and they're done with it. If the hotel's system then fails to actually record the information, the OTA has no way to know that. Ideally, the hotel would record it and only then reply "Ok", but I can easily see a system doing it in the wrong order.

On the other side of things, if the hotel's system fails to record the information, then they have nothing they can pull up to show that you even booked in the first place, which means that they won't charge you for something that (according to them) you never purchased.

The airline industry is likely at least a little different from this, because the bank did see the original authorization and it was just never settled. But the same type of failure could still have occurred between Expedia and the airline, leaving your tickets (and payment) in limbo.

I think it's a strong likelihood that unless you can confirm the ticket information with the airline itself (either on the phone or via their website) then your tickets don't actually exist, and you just need to start over and book new ones. You should also let the bank know so that if the charge does come through days or weeks from now, they won't honor it (and you should also watch your statements for a while, just in case). It sucks, but any time you're transacting through a third party, there could be a communication breakdown leaving you stuck.