Cold radiator/slow to warm up - tried everything (bleeding, balancing, sludge etc)

[Hot&Cold]

Is this the only vertical radiator on your system ? If you have more of the same width then exchange it as the kitchen radiator could be faulty.
What is the make of your vertical rad ?

you have not mentioned the heating system pump,this has to be on the correct speed and of a suitable head for your extended system.
you could check the adjustment of the auto bypass,it could be fully open and not allowing flow to furthest radiators. temporary close off the bypass valve and check if your vertical rad gets any hotter,then reset it to where it was (half way or there abouts).

Your kitchen radiator could be plumbed incorrectly but a few checks to eliminate the basics need consideration,

Good luck,

edit,last time opening a pdf here on this site fecked my laptop,so post photos

 

[D_Hailsham]

The pics are part of the pdf - you should be able to scroll down to see them

Doh!

The adjustable knob is an automatic bypass valve (ABV). It opens/closes as required to provide a path back to the boiler when TRVs close down, so the flow through the boiler is maintained. Is there a maker's name on the valve and can you see what setting it is on? If the valve is not correctly set, rads may not heat up sufficiently. As O&B suggested, close the ABV and see what effect it has.

Which boiler do you have (make and model no)?

The Grundfos (not Danfoss) pump is for hot water recirculation. Apart from being installed incorrectly, it is also not the correct pump for the job; it should be a Grundfos Comfort. I wonder if the installer had the Alpha2 lying around ...?