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I just withdrew £2800 from the bank. Looking at my online banking, there is only a withdrawal of £2000 listed. The form I signed said the amount I asked for, and the teller weighed the cash out on the scales to show the true amount, so my best guess is that she typoed it when entering it into the system.

Presumably this will be noticed at some point since the amount in the system is different to the form, but what are my obligations in the meantime? If I put the "missing" money in some sort of high yield account would I be able to keep any interest accrued? Should I inform the bank or let it slide until it is noticed? In the unlikely event that it's never flagged up, would not mentioning it be theft?

Update

I phoned internet banking yesterday as I couldn't find a direct number for the branch and couldn't make it back there before it closed. The helpdesk guy seemed a bit confused at me reporting an error in my favour, put me on hold and eventually came back to tell me he couldn't do anything from his end but would put a note on my account, and that I should tell the branch in person. I was also told that I was very honest and that I'd made his day as it would give him something to talk about.

Update 2
It's all worked itself out. There's a reversal of the £2000 transaction and a new withdrawal of £2800

Technically, you have no obligations.

You asked for £2800 from your bank, satisfied your bank's requirements (ID, having the funds, whatever) and you were handed £2800. You never lied or misrepresented anything and always acted in good faith. You are not required to connect to your online banking to double check the teller's work.

Now, that does not mean that you have won £800. The bank will notice the mistake and will put quite some effort into solving it, not only because of the money but because they want to make clear that the money is always under control (otherwise some employees may begin having bad ideas).

An £800 mistake is unlikely to go unnoticed in a small transaction, and there are probably very few transactions each day comparable to yours, so by the time the bank closes its doors they will probably know what did happen.

They can correct the movement by themselves (either by modifying it or by adding a new withdrawal); perhaps they will inform you (I am betting they will say nothing, because it will not affect you and maybe you will not notice it and nobody likes recognizing mistakes).

In any case, do not try to outsmart a bank. I know of a case (in Spain) where the teller mistakenly wrote an absurdly high amount for a deposit and, when it was corrected, the customer tried to use the receipts to claim that he had indeed made such a high deposit. The bank sued the customer for fraud. Banks do have lawyers, and banks do not have sense of humour. For example, do not try to withdraw all of your money before the bank discovers the mistake, and if the bank calls you and asks about how much money you did withdraw, answer sincerely.

Of course, apart from the obligations, you could always call the bank office and tell them what did happen, as a nicety to them and to save them some extra work and let them know that the issue will be solved in a civilized way.

Do you want a legal opinion or a moral one?

Morally

You should notify them as soon as possible or else some poor employee is gonna have a really, really bad day/week/month/year.

Legally

You don't have to do anything until they question you about the transaction. However, once it comes to light then you had better be ready to either have an additional £800 withdrawn from your account or give them the £800 in cash. They may even freeze your account until the investigation is over.

You have an obligation to tell them. That's not just a moral obligation; it's also a legal one. This has been proven time and again in court cases and criminal prosecutions, particularly when a defendant finds a way to trigger a bank error in their favor, and triggers it repeatedly. However, you have done that.

Regardless, as the old joke goes, "Haha, don't worry about it... They'll find you!" The bank is sure to catch up with this error, because they collect data about their money. You will see a $800 debit applied to your account. If you call in to object, they will tell you there's an explanatory note to that effect.

It's not like the poor teller finds the cash drawer $800 short at the end of the day. It's not a simple cash drawer. The machine knows exactly when it dispensed what funds, and it won't take long to reconcile that against the transactions that came through the teller's terminal.

That leaves the question of whether the teller embezzled the $800 or gave it to you. That's why they have CCTV on teller desks. Did the teller hand you a stack, or count it out bill by bill? That's not just for you.

As for the question of whether you asked for the $2800 or the teller just slipped it to you as part of a conspiracy, that's settled by the deposit slip and the audio recordings.

This will come about about as favorably as it can for the teller; they are neither an embezzler nor a conspirator to it. They made a simple error, and that's the trade-off when you employ humans for their other considerable abilities. What will concern the bank management is whether their overall error rate is beyond the human norms. You can't discern this from one data point.

As other answers mentioned, the bank will eventually find out and likely just withdraw the £800 from your accounts without notice.

Therefore, I would suggest that you make sure that you have >£800 balance in your account until this happens to avoid being charged any overage fees.

Let's have a go at answering the three questions posed in a factual manner.

If I put the "missing" money in some sort of high yield account would I be able to keep any interest accrued?

Yes - no problem with that.

Why?

Cash, indeed fiat money, is fungible - and I know that because I read fancy books on monetary theory!

There's no difference between "that" 800 and any other.

Should I inform the bank or let it slide until it is noticed?

I don't see that you have any obligation whatsoever to inform them, unless in your agreements with the bank, there's a clause saying that you should inform them in case of errors.

If there is no such clause in your contracts with the bank, then you simply have no obligation.

In the unlikely event that it's never flagged up, would not mentioning it be theft?

That is a very difficult legal question. (1) Jurisdiction? (2) You'd have to ask some real experts .. law.SE.