Not necessarily--everybody no matter what their immigration/visa status is entitled to free emergency care courtesy of the NHS.
This may be technically true, but "emergency" care is rather different than some places. The moment they send you somewhere other than the A&E, you are then responsible for paying, I believe. Often you go to the emergency, only to be sent over to an out of hours GP office. Or you might be admitted and kept in for longer, in which case, you'll be hating life without insurance. So yes, there is technically some access to the NHS, but nobody who is wise would rely on it.
All a moot point though as the OP qualifies.