This could push economic growth up to more than 2 per cent per year in 2019, 2020 and 2021, beating the current forecasts for GDP to expand by around 1.7 per cent per year.
However it would also lead to stronger inflation, encouraging the Bank to raise interest rates "a little more, a little sooner" than currently expected.
"If business investment growth were to recover much more strongly than currently projected – perhaps because of improved sentiment about progress on Brexit – then demand would grow well in excess of supply, pushing inflation above target throughout the forecast in the absence of tighter policy," Carney said.
This is not certain to happen, however.
Household incomes are rising faster than prices, which the Bank anticipates will boost the economy as spending increases.
However households reduced their savings and increased borrowing to keep on spending when prices rose faster than wages over much of the past year, so they may instead choose to save some of their extra spending power.
Alternatively, a breakdown in Brexit talks could harm the economy.
Carney stressed that the UK financial system is more than able to cope with any "cliff edge" departure from the EU, and said the Bank of England is ready too.
He hinted that likely actions in such an event could include cutting interest rates, as happened after the referendum.
"A sharper Brexit could put monetary policy on a different path. For example, if the transition were disorderly, or the end state agreement materially worse than the average potential outcome, then the MPC could once again be confronted by a trade-off between the speed with which it returns inflation to target and the support policy provides to jobs and activity," he said.
"On this path, the MPC can be expected to set policy to manage any trade-off using the framework it applied following the referendum."