feels like the steering is walking around mid corner/over bumps beibg pulled to either side and under braking is the same possible track rods then?
Any defects with running gear (bushes, bearings, steering, suspension etc) should have been picked up at MOT time.
If you don`t have a pair of correctly inflated, undamaged matched tyres of the same brand & type, & not part worns, on each axle as a minimum, though ideally all 4 should be the same, with the tracking set, then there is every chance you will be encountering these problems.
Blown gas shocks may have slipped through an MOT unnoticed though, they can make life entertaining.