I don't think that the government should pay for National Helath Services because if they were to, that would mean that they would have to actually get that money from taxpayers dollars and tax us more. I believe they should definitely subsidise it, but definitely not pay for it all together.
If the government were to pay for the NHS, the current level of taxation would only increase. At the moment it is completely funded by the public, which takes the strain off of the government even though it may slightly inconvenience the public. If it were to switch to be funded by the government instead it would place a greater strain on the government funds which could have farther reaching repercussions which would not be immediately noticeable. Lastly, even it were to be funded by the government, the taxes would still remain in place because the government would have nowhere else to obtain the money from.