CB doesn't set the cost of money at the moment, the market does. BOE increasing rates might temper inflation expectations of the market and lower costs. BOE reducing rates would probably increase costs in the short-mid term, maybe bring them down in the long term if inflation reduces.
No, businesses will pay down their debt and not take out additional loans, which will reduce inflation. They won't just carry on taking out more loans and expect to raise customer prices to pay for them. It would be foolish because customers are unlikely to be able to accommodate that rise in the current environment.
When young people say house prices are too high, they are normally met with stuff like why don't they buy less ipads and avocardo on toast. So now borrowing costs are too high why aren't they met by the same ? People buying in at high prices at the peak of the market is malinvestment. If you are rewarding malinvestment then that is going to have a huge impact on peoples choices and the consequences of the entire economy going forwards. It's called moral hazard.
The young people of today are going to suffer, to the benefit of the young people tomorrow, who will benefit from lower house prices and better affordability. Why should people in the future have to suffer to bail out bad choices in the present ? Homes should be homes, not for investment or speculation. Speculation only seems to work one way with property investors - happy while prices are going up, but not happy with the inevitable bust when things go wrong. Speculators should be taxed out of the marketplace.
For someone to be bailed out, someone else has to lose. So if rates are low, then the rates on interest paid to savers are low. Why should a person who has malinvested yesterday by taking on too much debt be bailed out at the expense of the prudent person who saved all their life, did not malinvest and now has their savings eroded by inflation running at 10% pa ? There are always winners and losers.
People in this country are obsessed by high house prices and encouraging people to "get on the ladder" even to the point of encouraging them to take on massive debt. We need to get house prices down and stop houses from being used as speculative assets by property investors. High house prices need to be seen as an economic failure. Not some sort of measure of success.
I do have sympathy for people who got sucked into the house price madness and bought with crazy schemes like "help to keep house prices high" or "help to make the unaffordable affordable". However I don't think they will end up being repo'd as it is just pointless. Just that their house/equity will end up being owned by the state with them effectively renting. That will help bring down prices across the board to the benefit of society as a whole, as there will be no engine to drive growth in price in higher priced properties.