LHMB - please don't feel dirty. The vast majority of women have had HPV! It's hard to estimate exactly how prevalent it is because it's usually symptomless, so women don't even know they've had it.
Estimates of prevalence vary from the late 70-something % to the late 90-%s. It's nothing to be ashamed of. 
birds - when you have a cervical sample taken, it now goes first for HPV testing. If you are HPV negative, you are clear. If you are HPV positive, they will examine the same sample for cellular changes (as was the case with the old smear). This is clearly explained in the leaflet you receive with your invitation and it has been adopted because it's now considered a more accurate way of screening women!
Just because you are not sexually active does not mean that you don't have HPV. As I explained previously, it can lie dormant in your system (with no symptoms) and flare at a later point (causing symptoms). Ongoing testing is therefore advised for this reason. Of course, if you don't want to take up the offer, that is always your prerogative.
Friend - it can take the body a while to clear an HPV infection, but there are plenty of women who have that same experience and who are fine. Please try not to worry!
Boo - I'm so sorry you've been through that, it can be really emotionally tough. 
Obviously, without knowing details of your case I can't really comment. Generally speaking, the sensitivity and specificity of HPV testing has really improved over the years.
"If almost every sexually active person gets HPV at somepoint, how can they unpick that as a definite cause of cervical cancer?"
It's not having HPV or not having HPV that matters. It's PERSISTENT, ACTIVE HPV. When the virus lingers around, it starts to cause cytological (cell) changes. This is not the same as it being dormant (when it doesn't 'do anything' in the body) - it's the virus being present in an active state for a longer time that causes the problem. 