There are many reasons why the wireless connection would be lower then wired.
1. the location of the livebox (near metal objects or magnetic fields)
2. Local radio interference
3. the line provided by BT (ask them to check it)
4. filters faulty (change it)
5. the reported speed is acually incorrect)
what it would not be is the network card or the livebox it they are talking to each other. What you need to do is ping the PC click here