Neither bank was expected to change their interest rates, but markets were on alert for any signs of future moves in monetary stimulus or shifts in the economic outlook.
The pan-regional FTSEurofirst 300 stock index sagged 0.3% as all the major bourses dipped, while benchmark German Bunds were virtually unchanged.
In currencies, both the euro and sterling were able to claw back some of ground they have conceded to the dollar in recent days. The latter has been pushed high by strong US data.
The pound looked the firmer of the two gainers at $1.6469. The euro was up 0.3% at $1.3600, but with euro zone inflation bumping along at very low levels, HSBC FX strategist David Bloom expected the ECB to reiterate it remains on guard later - a move that could weaken the currency.
"I would say at least some dovish rhetoric from the ECB, but from the Bank of England we are not expecting much at all. I think this mini dollar-rally, on the view the Fed is going to taper (the amount it pushes out as stimulus) and the ECB is going to loosen (eventually), is going to stay with the market."
ECB chief Mario Draghi has been at pains to stress in recent months that the bank is prepared to ease its record low interest rates even further below 0.25% and test out other, more unconventional, policy options if necessary.
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But this year has started strongly for many parts of the euro zone. Germany's economy is gaining strength and bailed-out Ireland has seen a strong return to borrowing markets, which in turn has lifted Portugal and other 'periphery' members.
Britain looks to be improving even faster. Some traders suggested the Bank of England could release one of its rare post-meeting statements to acknowledge the progress, though HSBC's Bloom doubted it would.
The BOE makes its policy announcement at 1200 GMT, with the ECB due at 1245 followed by a news conference at 1330 GMT.
ASIA WOBBLES
In Asia, shares once again wavered after a lacklustre performance on Wall Street overnight following Federal Reserve minutes and ahead of the US jobs report due on Friday.
At the same time, market reaction was muted to a slowdown in China's annual consumer inflation in December, which decelerated more than had been expected.
MSCI's broadest index of Asia-Pacific shares outside Japan shed 0.4% after snapping a five-day losing streak on Wednesday. Despite a weaker yen, Japan's Nikkei benchmark shed 1.5%.
Among commodities, gold was a tad higher at $1,227.05 per ounce, steadying after losing two days in a row and touching a one-week low on Wednesday.
US crude futures advanced 0.3% to $92.62 a barrel, rebounding from a five-week low hit overnight after data showed a large build in stockpiles at the US benchmark delivery point.
Brent crude also gained 0.3%, to $107.52 per barrel, while growth-attunded metal copper slipped 0.93% to $7,275.50 on its way to a two-week low.
"I'm a bear on copper prices - I think $7,000 is a more sustainable level," said Helen Lau, a senior commodities analyst with UOB Kay Hian in Hong Kong.
"The dollar will continue to strengthen because of U.S tapering (stimulus withdrawal), and China's economic growth is slowing down."