It is not taxes. The ba.com fare machine is quoting you a completely different base fare before applying the UUA.
What you need to do is make the WT+ booking at the cheapest fare rate and then immediately online (if it allows you) or by phone, use your Avios to UUA. Remember that you have a 24hr grace period to cancel an online booking free of charge if it all goes pear-shaped.
The extra taxes will be about £60-70.