The speed checker is based on what Openreach(BT) suggest is possible for your line. It tends to err on the side of caution - quite rightly so.
If you are currently getting 16MB then there is no real reason you shouldn't get that with another supplier.
However, I would take a snapshot of your current modem settings especially the SNR in case they have been tweaked a little, then any problems just refer to them for your new supplier.
Woody (chuntering along in his own inimitable style, using 100 words when 10 would do)