Can you feel the same play if you grab the compound and push/twist on it? It's not clear where the play you're feeling is coming from, this could just be the t-nut underneath the QCTP is not a tight fit (no big deal). (I'm not sure if this lathe uses a t-nut or just a threaded hole). Try completely removing the QCTP and seeing if you can identify the location of the play. There may be a simple fix.
It may then be a major repair, but worth investigating further. It could be something as simple as a chip caught between the carriage and the bed lifting the carriage up and out of place. Does the play change depending on the where the carriage is on the bed, near headstock vs near the tailstock? Are the ways showing signs of wear? Probably worth taking the carriage apart and cleaning under it. Then checking the fit without the apron and cross slide on it.
Of course, even a with a worn saddle and bed the lathe may still work fine for a lot of work.
Check that 4 and 9 are adjusted properly. It's hard to tell from the diagram, but it looks like they might be adjustments for the slides on the ways. Maybe not, but if you have a manual I would suggest checking to see if there is some adjustment that can be made.
Thanks,,,,,,, Ive always thought there was a problem with it due to the way it cuts, I'll pull it apart and have a look, Ive look in the book and no mention of adjustment of that part
Im surprised there is no adjustment on that part as they've made everything else adjustable