When you got the car you should have filled the top section out, Blue section, that is the section that should have been sent to the DVLA to inform them of any Owner changes, the green bit is for you to keep incase you get pulled by the fuzz, as for whether you can get Tax with it I really don know

Nice Polo, woul be cool if the light were really green

P.S, It doesnt have to be signed by the last owner...