I appreciate you can experience difficulties calling 0845/0870 numbers from outside the UK.

Would the same problems arise if you were to call a 0844 number?

It will depend on the providers in question routing the calls, rather than the IQ of any Ofcom employee. Some networks simply haven't defined it as a destination.

There are plenty of similar occurrences - calling a French hotel's 0892 from here, possible with Orange but not 18185.

Or some foreign mobiles can't be reached from all networks, also due to new exchange codes, or are charged as landlines, (even from BT and Skype).

I was in France years ago, when all the UK numbers were in flux. I tried to call from a callbox to a UK mobile roaming in France. I had made 3 similar calls earlier, but this time eventually I spoke to the operator. British numbers have just been changed and all start with 1 she said; no, I said, some landlines start with 2 5 8 or 9, but this is a mobile and starts with 4, and other mobiles with 3 and 7. So, even a national operator can get it wrong sometimes.

If you really need to guarantee reaching UK 08 or similar numbers from outside the UK, use a callback service that you know will reach them, thus making you independent of local conditions. This is how I called +44845 from one foreign GSM network last year. Then I used Enlinea, now I might use Voipfone.