Nov 14 (Reuters) - UK ministers are expected to order an in-depth investigation of Nvidia Corp"s (NVDA.O) planned 30 billion pounds($40.24 billion)acquisition of British chip designer ARM over antitrust and national security concerns, the Sunday Times reported. Britain"s Digital and Culture Secretary Nadine Dorries is expected to instruct Competition & Markets Authority to undertake a "phase two" probe of the deal next week, the report added.