Chinese national trying to improperly influence politicians, says MI5

Is there a formal distinction between lobbying and this activity?

The article is also fuzzy about the reasons why this is presumed illegal:

> Gardiner also employed a son of Lee’s as a diary manager. He said the son had resigned after MI5’s disclosure. “The security services have advised me that they have no intelligence that shows he was aware of, or complicit in, his mother’s illegal activity,” Gardiner said.

> The government is planning to bring in a new espionage legislation to update the Official Secrets Acts. Dr Alan Mendoza, the executive director of the Henry Jackson Society, said the Lee case demonstrated that the bill should be brought forward urgently and “that Britain’s arcane espionage laws require urgent updating”.