"Maybe we need a bit of a jolt to the system to remind us that trade is important," Mr Bailey said, adding he hoped the likes of deals between the UK and US, and the UK and India, would help to "rebuild the world trading system".
On Thursday, the UK and US announced a deal to avoid tariffs on certain goods in order to boost trade.
As it announced the latest cut in interest rates, the Bank said that while a trade war could hit economic growth, it could lead to lower inflation in the UK over time as countries such as China look to divert cheap goods originally bound for America.
Mr Bailey said the path for rates was "downwards", but said future rate cuts were likely to be "gradual and careful".
The minutes of the Bank's meeting showed the rate-setting committee was divided. Of the nine members, five voted to cut rates to 4.25%, two voted in favour of a larger reduction to 4% and two voted for no change.