Actually the current border of Iraq/Iran for the most parts dates back to the 1639 (Treaty of Zuhab) of which the King of England had a hand in negotiating between the Ottomans and the Persians.
Blaming the Brits for everything is a national pastime in many countries, it is the ultimate "Get out of Jail card" for most of the Nationalists in the old Empire. If you eff up, just blame the Brits for it.
Personally, I blame Alexander the Great. If he had come up with a viable succession plan, the Middle East would never have been divided between the Seleucids and the Ptolemies.