Does the "promise to pay the bearer on demand" mean anything?

An interesting point arose at church this morning. Get out a £5 or £10 note and look at it. As you probably remember from some time ago, it says "I promise to pay the bearer on demand the sum of X pounds" and this promise is signed (often) by one Mervyn King, Governor of the Bank of England.

What does it mean? I was taught that it used to mean that if you turned up at a bank and asked appropriately, they would give you the appropriate monetary value in gold. But with the end of the gold standard, donkeys' years ago, this, I assume, no longer applies.

A Bank of England document says:

In essence, the promise is that the stuff that you buy with this note does not change much from year to the next.

(Some promise - what if inflation goes hyper all of sudden?) But it doesn't say that does it? It says that Mervyn King, if you walk up to him with a fiver, will pay you five pounds. Presumably he would just give you a fiver back.

It is all very perplexing. I can feel a Ken Dodd joke coming on:

What a wonderful day for everybody in England to walk up to Mervyn King with a fiver and say: "Give us a fiver like you promised mate".

UPDATE: I have done some further digging and find from the Bank of England website that the promise is to pay five pounds in "gold or coinage". Also, ThisisLivingstonemusic.net gives this overview of the situation:

"I promise to pay the bearer on demand the sum of......"

On a bank note it states "I promise to pay the bearer on demand the sum of......". What that means is, the bank has pledged to the holder of that note, that on demand, they will give to the holder, the value stated on the note in gold or coinage. A bank note is merely an IOU. Therefore you are perfectly entitled by law, to ask for your bank account's total value to be paid to you in gold or coinage - it states it on all bank notes and is authorised by the Chief Cashier of each bank. So, that means that everyone is entitled to have their money given to them by their bank, in gold or coinage. The only problem is, there is nowhere near enough gold or coinage in circulation to honour these pledges, which means in effect, the paper money is worthless. If you want some entertainment, I suggest you ask your local bank for a £10 to be paid to you in Gold. The look on the young clerk's face will be all the entertainment you should have for one day.....

Here's what the Bank of England states....

Legal Tender and the Promise to Pay Legal Tender

The concept of legal tender is often misunderstood. Contrary to popular opinion, legal tender is not a means of payment that must be accepted by the parties to a transaction, but rather a legally defined means of payment that should not be refused by a creditor in satisfaction of a debt.

The current series of Bank of England notes are legal tender in England and Wales, although not in Scotland or Northern Ireland, where the only currency carrying legal tender status for unlimited amounts is the one pound and two pound coins.

Promise to pay

The "...Promise to pay the bearer the sum of ..." on Bank of England notes has nothing to do with legal tender status. The promise to pay stands good for all time and means that the Bank will pay out the face value of any genuine Bank of England note no matter how old.
The promise to pay also holds good for damaged notes, as long as enough of the note survives to prove that it was genuine and no previous claim for it has been received. The Bank's mutilated notes department receives some 25,000 claims a year for anything from fire or water damage to notes eaten by all manner of household pets.