I don't know anything about NHS, but I only have 1 tube (1 ovary as well). I conceived my dd after 7 months, so I'm certain it's not currently contributing to my infertility.
My friend has 2 ovaries and only 1 tube. It took her 4 months to conceive.
So, I wouldn't worry the slightest bit.
I know that I can still get meds for IUI with only 1 ovary/tube, so I can't see why you wouldn't be able to do it.