The tailstock is adjustable so you can turn tapers.  Sounds like it needs centring.  On my 280 there are two opposing allen head adjusters on the lower rear of the base:

They’re turned in opposition to swivel the top of the tailstock.

Dave

This problem arose sort of overnight.

Right:

Leave suspecting the machine to last and desperate! It can’t have drifted out of adjustment over that short time.

First and simplest, as Diogenes says, ensure cleanliness of the fittings. Brass can be ‘orrible, creating tiny needles that can get anywhere to interfere with correct fits.

Next, investigate the facing of the bar.

Even a very tiny pip left in the middle can be enough to push the centre-or spotting-drill fractionally to one side. This can arise with HSS tools if you sharpen them in mid-batch, even if only a light honing of the edge, so effectively lowering the edge.

I find it also be from slight inadvertent movement of the adjuster on a quick-change tool-post, or of shims on a conventional, simple tool-clamp. The main, but not obvious, source of vertical misadjustment on a QCTP is from turning the height-screw slightly with the locking-spindle, if the screw is not fully locked.

I always take a test facing cut, and reset if necessary, to ensure no central pip. That will affect both HSS and carbide tools, of course.

Also examine the centre-drill / spot-drill/ main drill. Has it blunted slightly unevenly?

The main drill is more likely to do that, but it takes only a tiny bit of unsymmetry to make it wander a touch.

Andrew has mentioned a very important point, when working on brass Stone the edge of the drill back so that it has no rake, ie it is at 90* to the work, this will stop it corkscrewing into the work, often with bad results. Try to avoid at all costs having to open out a hole as it is very likely to be pulled straight into the work. Good luck. Noel.

By coincidence I managed this blunder this morning:  nipping a drill off centre in the chuck.

The photo is staged to highlight the mistake – in real life the error wasn’t so obvious.

Don’t trust anything, check.  Some twist drills I bought at a show were bent.

Dave