Since I imagine he would make a massive fuss, Sylvia would allow a recount only in a few boroughs that Norrell can actually point to as being fixed, but that's mostly for the sake of shutting him up. It won't make a difference to the results.

If you want Norrell to do anything more about it, then that would be a discussion with the people who rigged the vote! That's Nancy, though I think Eames was involved as well...