Absolutely! The same airspace restrictions that are in the US are regulated by the FAA and ICAO. The FAA (or the US) is a signatory to the ICAO standards, and as part of that governing body instituted the same rules worldwide. Those restrictions are also issued through the NOTAM system.
Incidentally, flying in the UK, we had restrictions on where we could fly depending on where the Queen was flying (if our missions coincided with her flights). They even had a rather unflattering name for those flights in the pilot community.
Here is an article that talks a little bit about th e roles and responsibilities of the Queen's pilots.
You can also check UK NOTAMS (although i don't see any current ones fo rthe Queen at the moment).