Ooof.
The BOE sets the base rate. Not the lending rates. Competition sets the lending rate.
Your assumption is the lenders just accept less again in order to support your reduced payment.
Its possible but its far from certain.
Someone is paying in order for you to pay less. The question is does that person support your want or not.
If not then your likely going to see increased borrowing rates elsewhere.
How many times do I have to say this. LISTEN and respond to what I am actually saying.
The BoE creates a new, secondary base rate. This applies only to remortgage borrowing (and could include other criteria as well if we wanted, such as LTV threshold, term length, how recent the purchase was etc).
Mortgage lenders (i.e banks) are able to apply this lower base rate to remortgage products only, and are then able to lend off that rate. They still make a profit because they are borrowing off the secondary rate. Nothing changes for them.
There is no government department handing cash out to people. Its all done via BoE creating a specific market for this specific thing, and then the banks draw off it using their own existing processes. So government borrowing does not increase AT ALL in this.
What does happen is the lower lending rate for remortgages means that slightly less money is pulled from the economy than would otherwise be the case, so over time there is not as much of a decrease in money supply as there would be otherwise. But, it means no massive mortgage shock so some money still kept in the economy to support jobs and businesses.
The nature of people coming off existing fixed rates and onto this new product would mean that this impact on inflation and currency value is fairly slow and steady. No big shock to money supply, the main base rate still applies to new lending (because those decisions are being made now and people can take into account their circumstances now). As all new lending is still based on the main base rate, the desired slow down to combat inflation is still happening as well.
Once the turmoil is over and the main base rate settles, or comes down, or as people's pay rises catch up, and as existing mortgage holders get further into term with lower LTV over time, the secondary rate will naturally become redundant and people will eventually move back onto normal deals.