They have a political incentive to manipulate the base rate in order to win favor from the public (e.g. lower rates in the lead up to elections). Markets begin to mistrust rate decisions, and expect the Bank to pull the rug from under their feet. In summary anyway, no time to write a full explanation.
Edit: right, I'll expand on what I said, though not much as you could write a book on this stuff (as has been done many times).
Basically by not being independent and at the whim of government, Ministers may be tempted to exploit the trade off between employment and inflation- the Philips Curve. Bank cuts rates despite saying they will keep inflation at a target level, economy improves, jobs market improves, unemployment falls, inflation rises government well chuffed. Happens as it was unexpected. Except in the long run, the Philips Curve doesn't hold, and the market expects the Bank to go against its target for inflation. Therefore the higher inflation rate caused by the rate cut ends up becoming the 'normal' rate of inflation, which then has to be corrected, made difficult as the reputation of the Bank is damaged. This is very simplified, and I've missed bits out as it's been two years since I studied it (and of course being theory it's based on assumptions and a model). But hopefully it makes sense.