I've recently realised that my difficulties with a parting tool are mostly related to using one three jaw chuck. Closer inspection reveals that the jaws are ever so slightly bell mouthed, so I suspect the work is walking in the jaws.
The chuck in question is a Pratt Burnerd 160 mm self centreing three jaw. I bought new jaws for it – not convinced this has cured the problem reliably. I'm using an inserted tool courtesy of Jenny at JB tools, or a standard Eclipse parting tool 3 mm wide with no top rake. The lathe is a Mk 2 Bantam. I even modified the top slide slightly so I can lock the gib nice and solid. As far as I can tell the head stock bearings are adjusted right, though they could be a shade loose as I'm frightened of over cooking it. I don't think the Dickson toolpost is the best tool mounting for a parting tool, but its other advantages go without saying.
I bought a (brand new) 5 inch TOS chuck ages ago, but have hardly used it until buying a backplate recently to adapt it to fit on my Bantam. I just know if I say that this has been the cure for my parting off problems I will regret it, but so far so good.
Very – no extremely – not convinced about using power cross feed, but Andrew is right, you need to keep the tool loaded or it chatters like fun, and yes it's a mistake to slow the revs down more than say one gear (25% or so) to reduce the chatter and the heat on the tool, as the chip load goes up significantly. I part off with one hand on the cross slide dial and the other holding an oily paintbrush in the groove.
Hand number three is hovering over the stop lever.
Best regards
Simon