That doesn't match my understanding (based on chats with the missus and her sister).
One of the main reasons they had a constant drain on permanent staff, at the hospital trust my wife looks after, was because the agencies paid way over the market rate. Simple as that. Meanwhile, the agencies kept bumping up their charge-out rates to the hospitals (because there was nothing contractually stopping them doing so... i.e. weak procurement...?) which in turn attracted more permanent staff over to the dark side. i.e. it was a vicious circle. Last year, a cap on agency fees was introduced (can't remember by whom.... central government or the trust themselves?) and now the temporary/permanent balance is starting to re-adjust.