* Final March euro zone factory PMI 56.6
* Demand and optimism fell in the bloc but output stayed strong
* British PMI inched up from revised Feb number (Adds comment, details)
LONDON, April 3 (Reuters) - Europe's manufacturing boom stumbled in March as optimism waned and demand ebbed owing to a powerful winter storm, surveys showed on Tuesday, but expansion was still broad-based across the continent.
Factories in the currency bloc ended 2017 with record strong growth, so any slowdown from that pace is unlikely to stop decision-makers at the European Central Bank moving away from their ultra-easy policy stance.
In Britain, deep in negotiations to leave the European Union, manufacturing growth cooled to a year low in the first quarter of 2018, but a survey there suggested the economy is on a slow but steady course a year ahead of Brexit.
The March survey showed growth in cost pressures for UK factories and their selling prices cooled, something that may reassure Bank of England officials who are keeping an eye on inflation pressures.
Most economists polled by Reuters think the central bank is likely to raise interest rates to a new post-financial crisis high of 0.75 percent in May.
IHS Markit's final manufacturing Purchasing Managers' Index (PMI) for the euro zone sank to an eight-month low of 56.6 in March from 58.6, in line with an earlier flash estimate and still comfortably above the 50 mark that separates growth from contraction.
An index measuring output, which feeds into a composite PMI due on Thursday which is seen as good guide to economic health, fell to a 16-month low of 55.9 from 59.6, a little below its flash estimate.
Euro zone economic growth has already peaked, a Reuters poll found last month, but the ECB will probably decide this summer to slash its bond purchases if things develop as expected, policymaker Ewald Nowotny said last week.
"Clearly, the big question remains what the PMI will do next: the level is still good but the trajectory needs to stabilize in April," said Greg Fuzesi at JP Morgan.
Britain's PMI inched up to 55.1 in March from a downwardly revised 55.0 in February, beating the 54.7 consensus in a Reuters poll of economists.
"March's heavy snowfall doesn't appear to have had a particularly severe impact on supply chains," noted Ruth Gregory at Capital Economics.
"However, on the basis of past form, the output index still points to a slowdown in manufacturing growth to around 0.5 percent in Q1, well below the 1 percent plus rates seen at the end of last year."
A Siberian weather system British forecasters dubbed the "Beast from the East" brought snow, strong winds and the coldest temperatures for years to many regions.
Earlier sister surveys showed although growth slowed in the currency union's four biggest economies it still stayed strong.
Yet factories were at their least optimistic since the end of 2016 and demand for products was at its weakest in 16 months.
Some of that fall in demand may have been due to manufacturers increasing prices again while a strong euro probably played a part in making the bloc's exports less attractive.
In February, factories had raised prices at their fastest pace in nearly seven years. An index measuring output prices remained high at 57.3 in March, down from 58.4 a month before.
Inflation was 1.4 percent last month, official flash estimates due on Wednesday are expected to show according to a Reuters poll, still well below the ECB's 2 percent target ceiling. (Editing by Catherine Evans)