The Consumer Prices Index (CPI) rose to 3.7% in December from 3.3% in November, official figures showed today.
The Bank has battled with stubbornly high inflation all year, which it believes is being caused by temporary factors, such as spikes in commodity prices and January's VAT rise from 17.5% to 20%.
CPI has been above its 2% target every month since November 2009.
The Monetary Policy Committee (MPC) has resisted raising its base rate of interest from its all-time low of 0.5% despite growing pressure.
Jonathan Loynes, chief European economist at Capital Economics, said: "December's worse-than-expected UK consumer prices figures will do nothing to comfort those concerned that the MPC is neglecting its inflation-targeting remit.
"After all, the committee will have had the headline figures - showing CPI inflation rising from 3.3% to 3.7% - at its meeting last week."
The big freeze pushed up the price of vegetables in December as supplies were choked by disruption to the supply chain and crop damage.
The ONS said cauliflowers were particularly badly hit by the Arctic weather, which caused a shortage that led to a 75.6% rise in prices.
There were price hikes across most bread and cereals, aggravated by the wildfires that wrecked Russia's harvest and caused the country to impose an export ban.
The price rises brought in by utility companies also started to feed through to consumers in December, with gas particularly badly affected, pushing up the cost of housing and household services by 1.4%.
Petrol prices also continued to rise to £1.22 per litre, said the ONS.
Airfares were up by 41.8% between November and December, compared to a 41.7% rise in the same period a year ago.
But there was downward pressure on pricing from clothing and footwear, where prices fell by a higher-than-average 1.9% as the havoc caused by the snow forced retailers to compete for sales.
Other measures of inflation also increased. The Retail Prices Index, which includes mortgage repayments, rose to 4.8% from 4.7% in November.
Sterling was around 1% higher against the dollar today as traders factored in the chances of an earlier-than-expected rise in interest rates.
Howard Archer, chief European economist at IHS Global Insight, said there was now increased pressure on the Bank of England to take a stand against inflation, having kept its base rate at 0.5% for 22 months.
He added: "There is clearly a growing likelihood that the Bank's Monetary Policy Committee will act earlier than the fourth quarter and possibly even before mid-year.
"The MPC could well decide that a small near-term interest rate hike would support its credibility by sending out the message that it is serious about its inflation mandate, but would not have a major dampening impact on growth."