It's a little wordy in the original, but possible, at least in AmE, or perhaps in Am journalese. If you use "the," then you need to set off the name with commas.Prime Minister of Great Britain David Cameron arrived in Egypt.
Do I need 'The' with 'prime minister'?
Not sure. It's certainly better than "Great British Prime Minister David Cameron ..." You could say, "Great Britain's Prime Minister, David Cameron, ..." Note the commas. But no commas with UK:Is it better to say: UK Prime Minister David Cameron ...'?
Thanks in advance.