The minutes of the December 4 and 5 meeting, published yesterday, also signal the MPC is relaxed about the inflation outlook.
They show the MPC was again unanimous in its votes to hold UK base rates at their record low of 0.5%, where they have stood since March 2009, and maintain the scale of its quantitative easing programme at £375 billion.
The minutes highlight MPC members' focus on the recent appreciation of sterling and their concerns about the economic impact of any further significant rise in the pound. MPC members also discussed the beneficial impact of the currency's strength in dampening inflation.
MPC members noted sterling had risen by about a further 2% against a basket of currencies in the month leading up to the December meeting.
Setting out MPC members' views on the risks posed by sterling strength, the minutes state: "The sterling effective exchange rate index was near the top of the range it had occupied since early 2009, and had risen by around 9% since its recent trough in March 2013.
"Although the extent of the final pass-through to domestic prices was uncertain, that appreciation would contribute to disinflationary pressure. But any further substantial appreciation of sterling would pose additional risks to the balance of demand growth and to the recovery."
A stronger pound makes UK exporters less competitive in overseas markets. It also reduces the cost of imported goods for UK consumers.
The minutes highlight the fact that the UK's export performance was weaker in the third quarter than the MPC had expected. And business investment rose by less than hoped by the MPC, chaired by Bank of England Governor Mark Carney.
However, reflecting a view on the MPC that the business investment picture might be improving, the minutes state: "There were increasing signs from business surveys and the Bank's agents that investment might be rising as expectations of a continued recovery in demand became entrenched."
UK gross domestic product rose by 0.8% in the third quarter. The minutes highlight the MPC's forecast that the UK economy will grow by 0.9% in the current quarter.
However, the minutes also underline MPC members' awareness of the challenges faced by the UK as it continues to attempt to rebalance towards greater external demand, given the weakness in the eurozone.
Detailing MPC members' discussion of this issue, the minutes state: "The net trade data had been weak over the past couple of years, reflecting in part demand conditions in the rest of the world.
"In the euro area, only a very weak recovery was in prospect and inflation remained materially below 2%, but a moderate expansion appeared to be under way in the United States and there were signs that growth in the emerging economies had bottomed out. It would be difficult to achieve a better balance of domestic and external demand as long as activity in the UK's main trading partners remained subdued."
The MPC said in August that it did not intend to raise UK base rates from their record low of 0.5%, at which they have stood since March 2009, at least until the International Labour Organisation measure of unemployment had fallen to a "threshold" of 7%. This forward guidance on rates is subject to caveats or "knockouts" relating to inflation and financial stability.
In its inflation report last month, the Bank forecast, if rates were to stay at 0.5% and the scale of its quantitative easing programme were held at £375 billion, ILO unemployment would fall to 7% around the end of 2014. However, it has emphasised that reaching this unemployment level will not automatically trigger a rise in base rates. Official data yesterday showed that the ILO unemployment rate had fallen to 7.4% in the August to October period.
The minutes highlight MPC members' view that changes to the Bank and UK Government's Funding for Lending Scheme, removing direct incentives for banks to expand residential mortgage lending in 2014, "provided support to the MPC's policy guidance by reducing the risk of triggering the financial stability knockout".