Broadbent, in a BBC radio interview following the central bank's decision to keep interest rates on hold on Thursday, said he was "fully absorbed by and very privileged to have the job I have at the moment".
The U.K. economy grew at the slowest pace in six years during 2018, and in February the BOE projected an even weaker 2019, with growth of just 1.2%.
During the first quarter of 2019 the United Kingdom economy probably grew by 0.5% due to businesses building up stocks ahead of Brexit, the Bank of England said - a faster rate than the 0.2% growth it forecast in February.
Policymakers on the Monetary Policy Committee (MPC) voted unanimously to hold rates in the first decision since the Government secured a six-month delay to European Union withdrawal.
The Bank of England has held interest rates at 0.75% as it revealed a growth spurt thanks to Brexit stockpiling, but cautioned the boost will prove to be temporary as uncertainty reigns.
BoE Governor Mark Carney later told a news conference that rates would have to increase more quickly than markets now anticipate - if the predictions proved correct.
But Mr Carney made clear his view that investors were too relaxed about the pace at which the BoE could resume its gradual rate increases to ease Britain off the stimulus of low borrowing costs that has been in place for more than a decade. The Bank is expecting growth and inflation to pick up over the next two years.
Mr Carney stressed that while the global economic outlook has improved, "domestic tensions remain".
Agents reported that Brexit is pushing down already weak business investment intentions.
Mr Carney said: "The latest business investment intentions surveys point to further declines over the next few quarters, which would mark the longest run of falling investment in the post-war era".
"The underlying path of GDP growth appears to be slightly stronger than previously anticipated, but marginally below potential", the BoE said.
It added: "As new Brexit deadlines approached, it was possible that businesses would continue to worry about adverse outcomes and delay capital spending as they waited for a resolution to emerge".
Should the uncertainty surrounding Brexit dissipate, the BOE's estimate of the neutral rate of interest - the rate which neither stimulates nor reins in the economy - would likely go up.
There is speculation that finance minister Philip Hammond could again look beyond Britain's shores to fill the role - potentially favouring former Reserve Bank of India chief Raghuram Rajan - or seek a first female governor for the BoE.
Steve Moore ‘bummed out’ over Fed board withdrawal
Earlier today, Moore expressed disagreement with Trump's call for the Federal Reserve to cut interest rates. In another in 2014, Moore said that if women were paid more than men , society could be destabilized.