Back wheel moving to left side

This almost always happens because of issues with the rear quick-release skewer. On a horizontal dropout frame, it needs to be holding the wheel in nice and tight.

Three things can cause it. One, you may have some axle protruding past the dropout that keeps the QR from being able to clamp securely. Two, the cam surfaces of the QR need some lubrication for proper clamping force to be reached. Three, a modern open cam QR may have found its way on despite being essentially incompatible with horizontal dropouts because they don't develop as much clamping force as internal cam ones.

This happens mostly when the left wheel cup gets a lot of tension from movement and pressure from pedalling hence creating friction that wears out the left wheel cup creating this lean to the left.

This is mostly first indicated by a wobbling wheel, as later on results to this. The other issue is worn out ball bearings. Worn out ball bearings create a difference in holding of the wheel axle hence can lead to the leaning if some of the ball bearings are worn out or missing.

Thanks a lot for the comments, they did help a little at the time but did not solve the issue fully. At the end I found there were a few issues with the rear of that bike.

The freewheel was wobbling a bit and had to be changed. The bearings of the hub had to be changed and the axle was bent so that was changed, too. Finally, the dropout was a bit bent, too on one side. After changing/correcting all of these the issue did disappear. But it was costlier than I had hoped ? Unfortunately I cannot be sure which of these was the main issue.