A lot of people don't want Britain to stop using pounds and pence because they think we will have less control over our money.
For instance, they say that politicians in France and Germany could choose how much tax we pay.
In other words, decisions could be made which are good for the euro but bad for Britain.
Also, some people don't want to lose the pound for sentimental and historical reasons. It feels like getting rid of something that is very British.
If it does happen, it will only be after a long and important discussion.
The Prime Minister, Tony Blair, has said that the people of this country will have to vote first, in a referendum, to say that they want to use the euro instead of the pound.