Illegal use of NHS is negligible.
Frankly, if someone needs emergency care then just bloody treat them and be done with it, like we already do.
For non-emergency stuff, why not simply furnish hospitals with a list of people eligible to go on their books, to be checked internally? No surveillance potential, of course, nor can anything even be gleaned from such a list as it covers everyone, everywhere. Also good for citizens and visitors on their own insurance. Exceptions can be handled as and when, as appropriate.
With info being sent to the regime* how long before they're catching Murderers? Fraudsters? Non-violent x/y/z-phobic gobshites? Ganja growers? People with unauthorised opinions? This is a one-way street no matter how slow we're going on any given day.
If this was really about money they'd simply enforce existing tax law and close loopholes. But turkeys, Christmas, etc.
* /reɪˈʒiːm/ noun
1. a government, especially an authoritarian one.