My first move would be to replace what looks like a bit of B&Q studding currently used for a toolpost stud, with a properly machined stud that is a snug fit in the bore of the 4 way toolpost.
That way, clamping down the tool holder on to the cutting tool should eliminate, or at least cut down considerably, the tilt to the tool holder that is currently occurring.
Alternately, depending what model of Denham you have, the centre height appears to be around 5". A 5/8" tool is pretty hefty for this size of lathe, so you may be able to fit a different 4 way tool holder with a floor on it, along with 3/8" or thereabouts cutters, thus eliminating the issue another way.
If you went for the latter, I would still get rid of the bit of studding and go for a plain snug fitting tool stud, regardless.