Why do we bother with the Bank Rate?

When I "did" basic economics at school almost 60 years ago, we were taught that in a free economy prices were fixed by supply and demand. I remember it clearly, because our economics teacher was obviously a practical countryman and illustrated it in terms how the number of eggs required to barter for a rabbit varied on the black market throughout the year according to laying habits of the hens and the breeding habits of the rabbits! This was in a time of rationing and price controls so this was probably one of the few practical examples available to him!
My father, an accountant, who didn't quite approve of the example (although we kept ducks and occasionally had rabbit for Sunday lunch), pointed out to me that this argument was true with most transactions in life where neither the buyer or the seller were subject to coercion.
The fact that today that the Skipton Building Society had decided to enforce a “exceptional circumstances” clause in their mortgage contracts and increase the rate of interest, illustrates the truth of what I was taught. The Building Society had tied their loan interest rates to something like 3% above base rate, which as we all know, is being held artificially low. Whilst there were plenty of borrowers at that rate, there were getting less and less lenders who were prepared to put money into the Society at around 2% above base rate. Obviously it would have not been possible for this to continue indefinitely, particularly if there was more money being withdrawn than invested. The basic rules of supply and demand were working exactly as they have always done; the sellers (lenders) wanted a higher price (more interest) and at the moment dominate the market. The buyers (the Building Society on behalf of the borrowers) would simply have to pay more. Hopefully, the rate the Skipton BS has set will now attract in sufficient money to fund all those who want to borrow; if not, no doubt they will make further adjustments. Of interest to me personally is what rate will they offer to savers, and which bank/building society will be the next to break rank.

So as I said in my heading, "What is the point of the Bank of England's Base Rate?" If it was a guide figure at which transactions were being carried out, similar, in effect to the published prices on the Stock Exchange or Commodity Exchanges, it would have some purpose. Whether I want to know the current price of gold,  copper, cocoa beans, bank shares or dollars, I can look up the the price from the appropriate exchange via the internet and get some reasonable idea of what I would need to pay, both now and in the future. If I want to know the price of borrowing or lending money, there is no such figure, because the Bank of England insists it is 0.5% which is not only untrue, but totally meaningless. Because of this meaningless figure, contracts based on it have become grossly distorted, resulting in the action by the Skipton Building Society. It is the Government's and Bank of England's fault that this has happened, no-one else's.
Perhaps the Stock exchange should publish a daily interest rate figure based on reality to be used for financial transactions. After all, they publish a rate (the FTSE100) which is used to calculate the value of equity based savings, why should they not publish an interest rate (or rates) for other financial transactions?
The Base Rate could then be left to wither on the vine as a mere academic curiosity!.