He added that two suspects – a 46-year-old man and a 23-year-old woman – remained on bail.
Both were arrested at Heathrow Airport after returning from a trip to the US, on suspicion of prevention of a lawful and decent burial, fraud by false representation and fraud by abuse of position.
Mr McLoughlin said: “I want to offer my utmost assurance we remain committed to thoroughly, and sensitively, investigating, and working with our partner agencies to ensure the families and those affected receive the help and support they need.
He added: “Investigations into allegations of suspected financial and fraudulent activity are continuing, with dedicated, specialist investigation teams conducting various lines of enquiry and following up on numerous leads and information.”
Peter Welburn said he paid £1,900 to Legacy for his wife Shirley’s funeral and received what he thought were her ashes on 23 December.
However, the former trawlerman said he was then informed Mrs Welburn, 72, was not cremated until 16 January.
Speaking about the delays in bringing charges, Mr Welburn said: “How long is it going to go on for? This has been going on three months. People are angry. Everyone is sick of it now.”