Speaking today at the Bank, Carney said: "Any agreement that reduces access to aspects of our largest trading partner is likely to reduce the level of economic activity in this country".
In its accompanying Inflation Report, the bank also downgraded its forecast for United Kingdom economic growth for 2017 from 1.9 percent to 1.7 percent, following disappointing GDP growth in the first and second quarters of this year, of 0.2 percent and 0.3 percent respectively.
Sterling - supported recently on hopes of an interest rate rise - fell back against the dollar in the wake of the Bank's remarks, by nearly a cent, to $1.3160.
The Bank of England has voted 6-2 to kept interest rates on hold at 0.25 per cent.
It is unlikely more rate-setters will join dissenters in voting for a hike, although there have been signs of a growing split on the MPC.
The case to increase interest rates is enticing because it could help to bring inflation down. It has been forecasted that the economy would grow by 1.6% in 2018 and this is a cut from the initial expectation of 1.7%, which highlights the "sluggish" growth that is expected. Kristin Forbes, one of the MPC (Monetary Policy Committee) members to back a rate rise in June, departed the group and was replaced by Silvia Tenreyro, an academic at the London School of Economics.
'Monetary policy can not prevent either the necessary real adjustment as the United Kingdom moves towards its new global trading arrangements or the weaker real income growth that is likely to accompany that adjustment over the next few years.
He said the drop in sterling following the Brexit vote had fuelled inflation.
Back in June, Mark Carney said that he was prepared to raise rates if United Kingdom business activity increased.
John McDonnell, the main opposition Labour Party's top economic official, attended the protest and called for the bank to set an example to employers by raising their wages.
British inflation is being supported by a Brexit-fuelled slump in the pound pushing up import costs - although the annual rate managed a slowdown to 2.6% in June from a near four-year high of 2.9% in May.
But while remaining above the Bank's 2% inflation target, it represented an easing from the previous month's 2.9%. Moreover, with inflation expected to rise, "households" would have to make decisions on what they spend their disposable income as there is expected to be low wage growth.
"As a outcome, the household saving ratio fell from 3.3% to 1.7%, its lowest level since the series began in 1963".