I see you are from England. Who did you get your bumper from?
First thing I do when I get new chromed parts is to lather it down real good with automotive paste wax and keep applying it on a regular basis. It seems the universal truth is that new chrome parts pretty much suck.
EPA requirements have pretty much destroyed the good "heavy" show chrome industry here in the USA, and the quality control in third world countries just isn't up to par with what used to be chromed here. The chroming process has some nasty chemicals.
Some vendors even go as far as to charge extra for "show" chrome. Basically because of all the regulations.
There are custom shops that will re-chrome a bumper for you. I got a budgetary quote from Advanced Plating, a local shop here in the Denver Colorado area, to rechrome my stock front bumper....
$850