Governor Mark Carney said it is "likely" he will have to write an open letter to Chancellor George Osborne on account of inflation falling below this level in next six months.
It follows UK CPI inflation falling to five-year low of 1.2% in September.
Acknowledging the near-term outlook for inflation is "materially lower" than expected in the previous report in August, Carney predicted a return to the 2% target by the very end of the forecast period.
Falling commodity prices, the depreciation of sterling and the weakness of the UK''s main trading partners have all affected inflation levels, he said.
The Bank''s forecasts also concur with market expectations that increasingly point to no rate rise until next Autumn: it predicts inflation is unlikely to rise above the 2% target even if a hike was delayed until that time.
Gilt yields slumped following publication of the dovish report, 10-year yields dropping five basis points to 2.18%. Sterling also weakened, falling back from $1.593 to $1.586.
Carney again stressed the Bank will only raise interest rates gradually: "We have highlighted repeatedly what really matters is the broad shape of monetary tightening over the medium term rather than estimates of precisely when monetary tightening will begin."
The comments came as UK wage growth (excluding bonuses) was shown to have outstripped inflation for the first time since 2009, after rising 1.3% between July and September.
On the prospects for the UK economy, Carney said the country remains "unique" among its main trading partners in maintaining economic momentum.
The Bank of England predicts 3.5% GDP growth this year when official figures are revised, followed by 2.9% in 2015 and 2.6% in each of the following years.