There is no dignity getting a Pap smear here, either through a private doctor or an NHS nurse. They don't cover you up, they don't have stirrups for your feet, they just ask you to spread your legs, and then do a clumsy and painful smear. In addition, they don't do breast checks for cancer. Both people who gave me a smear looked at me as if I were an alien (which I guess I am) when I requested one (although they're automatic in the States), and then told me to do my own breast exams. I know these things because I've gone both the private and the NHS routes. So I hate to tell you, but in that regard, things are drastically different here from in the States.
there is no 'dignity' in any of these procedures. they are medical procedures to help catch potential health problems.
like others, i've always been offered a paper sheet to cover me, but then again, after two vaginal deliveries i'm not really that bothered with modesty.
as someone with lower back problems after my second child was born, i've
very glad there's no feet in stirrups here for smear tests. personally, i find that far less dignified than the US procedures.
it shouldn't be clumsy or painful, except if you have cervical erosion - this usually comes from vaginal childbirth and resolves itself over time.
if you don't want a male to perform a smear test, groovy, you can have the practice nurse do it or go to your local FPC as Britwife suggested.