In a word, yes. The World Health Organisation defines privatisation as "a process in which non-government actors become increasingly involved in the financing and/or provision of health care services." This is indeed happening in the NHS.
10% of the NHS England budget is now spent on care provided by non-NHS bodies, including non-profits and private firms. Department of Health figures show that 7.7% of day-to-day NHS funds went to private firms in 2016/17, compared with 6.3% in 2013/14 and 2.8% in 2006/07. In addition, £0.94bn was spent on PFI payments in 2016/17. Private firms won 70% of tendered contracts from NHS England in 2016/17, and the total value of contracts going to the private sector jumped from £0.7bn to £3.1bn.
There's also the concerning matter of more patients paying for private treatment within NHS hospitals. NHS acute trusts made £583m from private patients in 2016/17, up from £487m in 2012/13.