A couple of main points with regards to Canada (I don't know how similar it is to England):
1. Who is responsible for monetary policy?
The inflation-control target — one of the two cornerstones of Canada's monetary policy — is set jointly by the Bank and federal government. However, the day-to-day administration of monetary policy is the responsibility of the Bank's Governing Council, composed of the Governor, Senior Deputy Governor, and Deputy Governors.
The Bank of Canada Act requires regular consultations between the Governor and the Minister of Finance on the direction of monetary policy. If a profound disagreement were to occur between the Bank and the government, the Minister of Finance could issue a written directive to the Governor specifying a change in policy. This would most likely result in the Governor's resignation. However, such a directive has never been issued.
2. How does the Bank of Canada implement monetary policy?
The Bank implements monetary policy by influencing short-term interest rates. It does this by raising and lowering the target for the overnight rate (also known as the key policy rate.) This is the interest rate at which major financial institutions borrow and lend one-day (or overnight) funds among themselves.