Their coffins were carried by fellow servicemen and were covered with Union Jack flags, or flags chosen by their families.
A full military band played while the coffins were carried off the planes.
Eight of the soldiers were killed when the US Sea Knight helicopter they were on crashed south of Kuwait's border.
The two other men were crew of a RAF GR4 Tornado which was shot down near the same border by a Patriot missile.
All over the UK on Saturday, families of soldiers fighting in Iraq will march in honour and support of them.
Many are annoyed so many people are protesting against the war. They feel they are not supporting the soldiers enough.
In Iraq there have been reports of another "friendly fire" attack by a US aircraft on UK soldiers.
It's thought one UK soldier has died and several others have been hurt in the incident.
But British officials have only said they know one soldier is missing after heavy fighting near Basra on Friday.