The answer is essentially, both of you.
you must ensure it's safe to pull out before you do so.
The taxi should not over take when they might come into conflict with other road users, and the Highway code explicitly states junctions as an example.
If the taxi was so far away when he started his manoever, you should have been able ot manoever and clear you manoever. If you collide he wasn't "so far away" after all.
If you'd pulled out, turned and were established on the major road, and been hit head on, then possibly a court might find you not at fault. If you had only just started to pull out when you hit the side of him, and the impact is largely on his correct side of the road, he might get away with 100%.
If it was a say, dual carrige way, and he was passing somehting you couldnt see through, and traffic was say, stationary, and say creating his own lane, perhaps to turn r further down the road, or looking to pull into a space he couldnt see into, and he couldnt forsee you pulling out, as say you were coming froma petrol station, not a turning, then that might end up 80/20 your favour.
However, I have an interesting one this week on my desk.
A careful retied ambulance driver, wants to pull out of a side road. Van stops to the right and a van stops also to the left to let her out. The van to her right, is at an angle, stationary, and indicating. The side road is just after a pedestrian crossing, with zig zags. However, the van cannot turn in, as the side road is narrowed, so the car pulling out "must" do so, without ensuring the way is clear. The main road is a single carrigeway in each direction. So the driver pulls out, and collides with an moped, overtaking the stationary van.
Who is at fault? I say the moped 100%. There was enough warning of the 2 stationary vans, the presence of a side road. The emerging vehicle had no alternative, (it was practically unable to reverse down the side road), and couldnt be expected to sit there all day blocking the side road. The mopeds riders solicitors say say 100% the emerging vehicles fault, but I think would accept 50/50 if we offered. I dont think thats fair, and we are proceeding to trial. If we lose, the claim with court costs is probably worth £35k, over settling it quickly against the van driver at say £5k.
What would you do?
I work for an insurance claims dept dealing with liability/personal injury.