I realise it is unlikely they will do it but what if they turn up with an excuse (e.g. a delivery, or something)  when I am not at home and my children or my wife opened the door? What if they trick their way into the property? Could they possibly do it or is it illegal?

I would just add, for the benefit of those enjoying the delights of CLI correspondence, they the first letters they sent threatened prosecution. Now they don't seem to follow through on that and they switched to the different threat of 'personal visit'...

does anyone have experience of CLI paying a visit?

I have ignored their letters and now I have receive a "notice of personal visit", stating that someone will come and try to find me, repeatedly, until they do.

I assume they have no legal power whatsoever, and even if they did find me I would be under no obbligation to let them into my property, right? 

I am inclined to keep ignoring them, unless someone has different advice?

so they are powerless, and all these letters they write are just a waste of time? Or do you have any experience of them taking any sort of bold action, such as trying to gain physical entry into a property or the like?

Do CLI have any power to raise a CCJ for a debt that they do not own, e.g. a foreign debt?