District Court judge Douglas Yau said the defence failed to prove that missing documents from securities brokerages and delays by investigators would result in an unfair hearing.
The hairdresser-turned-tycoon has denied charges of "dealing with property known or believed to represent proceeds of an indictable offence" between 2001 and 2007.
Yeung, dressed in a dark suit and grey tie, appeared calm but tired in court.
After the decision to proceed with the trial, the prosecution presented its case, saying deposits of about £60m made to accounts in the name of Yeung and his father far outweighed their combined income of £180,000 over the period in question.
There were 437 cash deposits made by unknown parties totalling about £8m for no apparent reason, prosecutor John Reading SC said.
The deposits also included cheques from a company operating casinos in Macau totalling £6m, he added.
Defence counsel Graham Harris told the court this week that Yeung could not receive a fair trial as he was unable to secure documents that might be crucial to the defendant's case.
Financial institutions in Hong Kong are required to keep business records for seven years, which means some documentary evidence that could support the defendant's assets and lawful trading activities may no longer exist, Harris said on Monday.
The trial resumes next Tuesday.
The case comes a week after Hong Kong's banking regulator said it was doubling the size of its anti-money laundering team to toughen supervision after two court cases drew attention to financial institutions' compliance and monitoring systems in the Asian financial centre.
Yeung, who heads Hong Kong-listed Birmingham International Holdings Ltd, was arrested in June 2011. Trading in shares of the Championship club's parent company has since been suspended.
The company had a market value of £50m before the trading suspension.
Hong Kong's anti-money laundering ordinance came into effect last April, empowering the city's monetary authority to prosecute or discipline banks for ignoring or assisting in money laundering, including fines of up to £83,000 and the revocation of licences.