ToughDaddy - It is a dangerous assumption to assume that players in the financial arena are "thick" (although after so many failed banks I can see why you would think so )
You assume that lower rates are good for banks, which is not necessarily true and depends on the bank (it's liquidity, operations, etc). It is good for banks who have high short term financing needs, but others make more money in high interest rate environments, especially from treasury and money market activities.
So not really "Prisoner's Dilemma", as low rates are not the best outcome for all banks.
The rational strategy at current environment of liquidity crises and uncertainty is to close the shutters, hold the fort, and wait for the storm to pass - which is what banks are currently doing.
Btw, bad debts look bad on the Balance Sheet, rather than the Profit & Loss Statement (P&L).
"Now their mortgage rates are a function of :"
- Risk assessment for the future.
This is the part that BoE is having trouble cracking, despite lowering interest rates significantly.
As long as banks feel there is a higher risk of default now than in previous years, interest rate cuts will be reflected in a muted manner to the customer, and that is an entirely rational game plan for the banks.