Army service records from 1760 - 1913 from the National Archives War Office WO97 class (Chelsea Pension discharge papers) are now available online from the subscription database Find My Past. However, unless you have a regiment, year and place of birth it would be exceedingly difficult to isolate him from all the other James Powell records. If you can find him in Birmingham in 1847, you may be able to do the same in the 1851 Census if his regiment was in England at the time. But again, the common name is against you - there were hundreds of men in the British Army named James Powell which could be narrowed down by a birth date if you had it.
Others have suggested the Medal Rolls at ancestry online. There are over 50 James Powell or J Powell recorded on the Crimean Medal Rolls - again a dead end if you do not know the regiment.