There are a lot of fallacies around rate setting. The first is that the BOE is somehow "independent" and can set its rate independent of the rest of the world. It can, but the consequences of this are that it would trash the currency, as all the money would move to countries that offer a higher return.
Currently the major western banks are all increasing rates (US, Canada, Europe), so we have to increase rates too. The primary driver at the moment is the US, but Europe are not so far behind. We have to keep our rates competitive with the US otherwise the currency is toast.
So the government has a choice, either trash the currency or plunge the country into a recession. The second of those is a better choice than the first (but the first might lead to the second and vice versa).
The real issues will start to come if the US cannot get its inflation rate under control. There are a lot of people who believe it did not start raising rates early enough, so now it will have to raise rates higher in order to crush inflation. In that scenario, we may be in a situation where the US continues to raise rates, and even though we have been plunged into a recession we will need to continue to raise rates along with them and Europe to stop a currency collapse. This could result in a sustained and prolonged recession (depression).
Most of this is fall out from the money printing we did after the GFC of 2007-2008. We used QE to mitigate the recession, which was probably the right thing to do. But unfortunately rather than using it to buy time to restructure the economy through the 2010s, we basically returned to our pre-2007 behaviour, building an economy again too dependent on credit and ever inflating assets such as house prices. This was encouraged by keeping interest rates far too low, and boosting the housing market with unnecessary policies like help to buy.
During the 2010's we had a great opportunity to let asset prices/house prices fall gradually and let the market reset and come to a better equilibrium point, but instead government policy and low interest rates pushed them ever higher.
Now we are in a position where we have no choice. We can't borrow or print money to bail out those who have taken on too much credit - the markets won't let us. We have to continue to raise rates to protect the currency, if we do it is likely to put us in recession, if we don't it will trash the currency. So it is a case of a hard object meeting a brick wall. There are no easy choices moving forwards.