Whooooaaa if the UK ends up with anywhere near same shite system of healthcare as the US, that's not good news for anyone. American drug prices are an absolute fucking scam and the American pharmaceutical industry is so incredibly predatory. You couple that with private health insurance and the entire healthcare industry looks like an awful awful scam here. Here I get my health insurance through work, but I still have to pay a fraction of it out of my wages - I think I pay about 4% of my paycheck into my insurance. I have good coverage, but it still feels like a ripoff. And in the U.S., I think most people don't have their employers pay for their insurance (I think it's 51% have their own insurance) - for them the costs are higher because they're paying 100% of that bill.
Right now even drug companies in the U.S. give preferential rates to Medicaid - their state run health system. For everyone else in the country, the rates are significantly higher for drug prices because they've negotiated with individual health insurance companies what the values of each drug costs. So @Stan is absolutely right, if the rate NHS pays for drugs is on the negotiating table, it is CRITICAL that the information about the pricing is made public.
If drug prices in the UK get anywhere near what they are in the U.S. - the NHS is absolutely fucked. The austerity goons will point to how expensive it is to maintain the NHS after these new drug prices come into effect, and then all of a sudden there will be a huge push for the dismantling of the NHS and selling facilities to private caregivers. This is after a bus was driven around the city saying the money we pay to the EU will go towards the NHS - so this is a pretty big betrayal to Brexit voters who may have believed that load of shite, and surely by now must have come to terms with the fact that NHS would in fact probably be working with a smaller budget after Brexit than what as promised (although those people were fucking true).
If we move to the U.S. model of healthcare, it's not going to be good for the working class - just like it's not for the working class in the United States (source: https://www.apexedi.com/medical-bills-the-leading-cause-of-bankruptcy-in-the-united-states/). It's also not good for business generally - there's lots of evidence that shows having a well working public health system (like NHS) means that employers don't need to provide expensive health insurance for their workers (because in a business perspective, a healthy workforce is a productive workforce - if you've got people that are constantly ill, that's people that you either need to replace, which costs money, or those workers are less productive because they're constantly ill, which costs money). And it's particularly bad for smaller businesses, as health insurance can be very costly - so that's a big chunk of capital that smaller businesses would be otherwise using to grow their businesses.
So really two opposite ends that feel the biggest brunt of that... assuming that these pharmaceuticals are interested in having UK prices be closer to what they are in the US. And even if it doesn't come close to US prices and is just a minor increase, any price increase means a higher cost to maintain the NHS at it's current standards.
As said above, the NHS should not and should never be a part of a trade deal with any nation. Especially not the one developed country with the predatory form of healthcare.