Replace tires on same axle
and they put a new one on the wheel
I am so pleased you backed up and described the problem you are having and those changes (new tire on one side) which you feel might be associated.
If there is significant wear then you should have replaced both tires on the same axle. What you may wish to do now (as a cheaper alternative) is swap your front and rear tires and see if this changes the sideways "pull" you're experiencing on launch. Be sure to mount your wheels so the tires are rotating in the correct direction (some tires are designed to roll one way).
There are many reasons for a car (especially front wheel drive) to want to turn when power is applied and each has their own cure. There are also many who are more qualified than I to discuss these problems in more technical detail. What I would like to do is spend a few minutes trying to convince everyone to remove the jargon and just describe the problem.
Torque Steer is definded as
A tendency for a car to turn in a particular direction when power is applied. Torque steer is common in front-drive cars because reaction forces created in the half-shafts can generate uneven steering forces in the front tires. See Also
Wiki Definition
So all other things being equal (perfect surface, perfectly straight, perfectly level, you know, perfect) then a car might have a tendancy to pull to one side a little bit. In the case of a 1969 Mini Cooper "S" perhaps more than a little bit.
but Torque Steer is gets the blame
The natural inclination of a vehicle to follow the path of least resistance is not Torgue Steer. By this I mean to follow a rut in the road or the road camber or to turn one way or another because one of the driven wheels has traction when the other doesn't.
The requirement to forcibly turn the wheel straight when exiting a corner (lest the vehicle continue the turn into the nearby wall). This also is not Torque Steer.
Conclusion
Several of the tracking and traction problems which occur most prominently in high performance front wheel vehicles are often misrepresented as Torque Steer. This is unfortunate because often those in the best position to provide advice are mislead.
As a competitive motorsports driver I have learnt always to simply describe the problem rather than attempt to use mechanical terminology. I once attempted to describe a problem I was having by stating "it's overly damped". I was so pleased with myself for having finally learned to speak the language but when I went back out on track I quickly found myself in the scenery!
