If I understand what you are asking the item you refer to as the middle silencer is the catalytic converter (or cat for short). It does have some silencing effect but it is not a silencer as such. The rearmost box is the silencer and removing that will effectively give you an unsilenced car. It will also have a huge effect on the functioning of the engine management system and may be so far off the limits of functioning of the fuel map as to risk damage to the engine in the long term.
If you want a better sound you should consider fitting an exhaust system from a recognised supplier that can also provide a re-map of the ECU to suit that exhaust system.
I see that Williams now have a system for the Duratec 2.0l engine and I imagine that they have a suitable re-map to go with it.
Not as cheap as fitting a straight through pipe but a much better solution and should give no problems for an MOT.