privatisation means hospitals that don't turn a profit will be 'allowed to fail' - i.e. shut. In order to avoid that, they will chase private patients. The government is lifting restrictions on how much private work hospitals will do. At the same time as removing limits on waiting times. So the rich will get swift, top-notch treatment, while Mr and Ms Average get sicker and sicker waiting for care. Which is what happened under the last Tory government.
Many hospitals are also nobbled because they've been dumped with expensive Private Finance Initiative deals - basically a hideously expensive way of building hospitals that has made loadsamoney for companies selling on the debt but is a massive drain on the public purse. Those hospitals will have even more need to boost their income from private patients.
Privatisation also drives up admin and transaction costs - all those contracts and complex payments cost money and take time to process.
As for 'we can't afford free healthcare' - actually private healthcare costs far more. The US pays a far higher proportion of GDP in healthcare costs, for far worse care and far worse outcomes. The highest performing healthcare system in the US is the Veterans Healthcare Adminstration, which is basically a mini-NHS for servicemen and women.