Why does dried pasta say "Do not reheat" on the packet?
Consider this as not backed by authority, more opinion, but I believe this is a case of caution because once hydrated and warm pasta can become a prime breeding ground for bacteria.  On reheating, you may well not get it high enough or high for long enough to kill any bacteria, and its density makes it even more difficult to remove any built up toxins those potential bad guys may have produced.

Now, is it a case of CYA?  Yup, more than likely, but I know in the case of rice there are many reports of food poisoning from cold and re-warmed, and I would think it is possible with pasta as well.  I still do it myself, but that is my choice.  I have also never noticed packaging that said not to, so this might be a labeling requirement not adopted in the US.

As for things like fried rice made from cold rice, not sure that one really applies.  To me that is cooking a new dish, not reheating and to me it seems like that is heating enough it should be safe.  Thoroughly reheating a dish like lasagna to normal serving temperature, especially if the original dish was not left in the danger zone for an extended time would seem safe to me also.  But those are opinions, not facts backed up by lab tests and it is possible UK health agencies have tested and do not agree.

ETA:  Pasta Safety is a posting I found after stating my opinion, and it details the risk.  Their claim is basically as long as it is refrigerated, 2-3 days should be safe, but not longer.  Bacillus cereus bacteria is the sited culprit.  Hmmm.  I personally would say refrigerate promptly and the 2-3 days is likely conservative, but again, that is opinion not backed by tests.