Fix or stay on my "dodgey" BBBR Barclays tracker

I have a 2.18 plus BBBR 0.5 lifetime tracker with Barclays/Woolwich.
Currently paying 2.68%

Now the problem is the BBBR is the BarclaysBankBaseRate which is not guaranteed to follow the BoE rate.

I could take one of the 5 year fixes (2.79%) for example..OR do I trust Barclays wont ramp up their BBBR and keep it following the BoE?

So I guess my question is...can (of course they could) or will Barclays ramp up their BBBR or would it cause them a furore.

thanks