The money laundering regulations went through Parliament on Friday
Ministers believe groups like the al-Qaeda network have been using bureaux de change to launder funds obtained through the drugs trade.
It is estimated that more than £2bn a year changes hands in this way.
The new money laundering regulations will give HM Customs powers of inspection and regulation of bureaux de change, cheque cashing companies and money transmission agents.
It is being launched as the government moves to introduce emergency measures to detain terrorist suspects without trial.
Legislation to crack down on bureaux de change went quietly through Parliament on Friday.
At present, anyone can set up a bureau de change but under the new regulations all such offices will have to be registered and approved by Customs and Excise.
Customs staff will also be given the power to carry out surprise inspections at money changing offices to examine their accounts.
Customs Minister Paul Boateng said: "Our aim is clear - to cut off the funds terrorists and criminals rely on to pay for their operations.
Frozen assets
"These new arrangements give Customs the powers they need to inspect businesses and stop them being used to launder the proceeds of drug trafficking and other criminal activity."
The UK-wide powers include:
Failure to comply with registration requirements, or to provide access to premises and records, could result in a fine of up to £5,000.
Government officials say that since 11 September, six bureaux de change have been raided and 16 people arrested for allegedly laundering a total of £120m.
Last month, the government announced new measures to freeze assets they suspected were being used by terrorist organisations, following the US attacks.
The move is part of an international drive to paralyse funding for alleged terrorist organisations.
Treasury officials have disclosed that £70m has now been frozen in 38 different bank accounts in Britain believed to belong to terrorists.