London for mothers?

On Saturday I'll be having a mother daughter day (awww bless) journeying to London with my mom to see Wicked at the Apollo Victoria.  I love London, especially when I'm not there for meetings, and so I can't wait to go as a tourist again...it's been well over six months since I've done that.  Too long.

So I asked my mom today what she'd like to see/do before the show: Harrods, Buckingham Palace, Towers of London, London Eye?  "I could do with a new summer coat.  Can we go to a few shops and have lunch?  I don't really know what's there."

Everything mom!  Everything is there!  My usual haunts of Topshop, Portobello Road and various markets will not suffice.  Please someone advise me where you're supposed to take your mother, who is not rich, to find a summer coat.  "Oxford Street" is too broad an answer.