10 mins isn't that bad. Arrived 17.30 LHR T3 (ex AUH) on Good Friday & it took at least 15 mins for Euro passports holders to get through immigration, whilst the 'alien' desks were almost empty & (mostly) staffed. And Good Friday was a quiet day. Delays regularly occur at T3 for Euros where, guess what, there are only principle two desks.
You can get into Saudi Arabia faster as an alien and they really do have strict immigration procedures.