I am going to go for carpet cleaning london first, then when I am there im going whole hog for carpet cleaning
London I can understand (and surprisingly few are really going for it).
Why on earth would you want to rank for just "carpet cleaning"?
Because there are 1.2 million searches a month for carpet cleaning and locally there are 870,000 searches Carpet cleaning London there are 14,800 local searches.
Where as when you go for some keywords like carpet cleaning Portsmouth, there are probably 280 searches a month, not much to go after.
Although there are 1300 searches for your area Birmingham.