Mick Jagger and Dave Stewart have composed theme music and written three original songs for “Alfie,” Paramount’s remake of the 1966 comedy-drama starring Michael Caine.The songs — “Old Habits Die Hard,” “Blind Leading the Blind” and “Let’s Make It Up” — were written especially for the film and recorded last week at Abbey Road Studio 2 in London. Composer John Powell is teaming with Jagger and Stewart in including the songs in the score. “Alfie” stars Jude Law, Marisa Tomei and Susan Sarandon; Charles Shyer directed. Par, which plans to release “What’s It All About, Alfie?” later this year, is calling the pic a “reinvention” of the original. For the original “Alfie,” Burt Bacharach won a 1967 Grammy for instrumental arrangement for the perf by his orchestra.