When travelling abroad, would the British Prime Minister carry a red
brief case/ attache case similar to that displayed by the Chancellor
of the Exchequer on budget day or would it be a more personal or
different official type of case? Would he have any other form of
luggage with him.

The red attaché case exhibited by the Chancellor of the Exchequer to
press photographers each Budget day is, in fact,  a "red box" of the
kind used by all UK Government ministers to carry official papers away
from their offices. Often the papers are so voluminous that they would
occupy several red  boxes; and whether a minister would carry them
personally would depend on the circumstances of their trip. For
example, if he or she was going on a private weeked trip in their own
car, yes they probably would take the box or boxes themselves. But if
it was a minister - especially the Prime Minister - going on an
official trip abroad, then almost certainly a minion would take care
of the red boxes. ("Bag carrier" is a term often used for a lower
grade civil servant accompanying a minister.) Incidentally, you may be
interested in this article about a new hi-tech red box -
http://www.prnewswire.co.uk/cgi/news/release?id=55454

Tks Geof this was an enlightening and helpful response

I understand that these cases are made by this company:
http://www.swaineadeney.co.uk/perl2/v2.cgi?sectiontoken=attache-document-cases

I once asked there about a case that had the handle on the hinge side
of the case and was told that it was for ministers; allowing his "bag
carrier" to place the case in front of the minister so that he could
open it immediately without his assistant's seeing the contents.