A goatee and a suntan go a long way. Try to not look obviously European.
Unfortunately, Tony Blair's legacy of Poodle-ism means that us Brits have to watch our step in some places.
Notwithstanding that, I've generally found the vast majority of Muslims to be generous, welcoming, curious and friendly around the Middle East.
I have had two incidents of hassle in six years of residency in the region, and they were not serious, more like local guys yelling at me after a particularly brutal act by the Americans in Iraq or Afghanistan (bombing a wedding party, killing kids, that kind of thing).
When asked as to nationality I often say I am Irish these days.
The main issue you may have in Iran is at the border and police. If they pick up on you being ex forces they may suspect you of spying. You may be discretely observed regardless.
'Peaches are better than Tanks'