OK, and update. Sorry it's a bit long-winded.
First off, our TRV is Bulldog and I do not know if it is bi-directional because I cannot see any direction arrow cast on the body of the valve - and I have spent some time looking.
OK, I update, based upon what I have found out since.
I turned all the rads in the system off by turning their TRVs down to 0.
I left the kitchen rad on full by TRV with the heat pump running and the room stat turned well up.
After five minutes the pipe under the TRV started to heat up and eventually became quite hot, though not so hot as the pipe under the lockshield valve.
The rad itself became hotter, with heat eventually returning to the bottom half of the rad, though it never got as hot as the top of the rad.
I took the head off the TRV and pushed the valve up and down for quite a long time. I gave the valve stem a couple of taps with a spanner.
I listened for the pump by turning the TRV valve up and down (0-5). On 4 and 5 you can hear the pump using a screwdriver to your ear on the top rad valve on the lockshield side. Any lower than 4 and you can't hear the pump.
During the time I had all the rest of the rads on 0 by TRV, the pipe under the lockshield valve got very hot indeed - much hotter than the pipe under the TRV, though the latter did become quite hot itself.
My father in law (MK2) says he thinks that it's a sticky valve, but I disagree with him because:
With all rads turned off the water in the return would be hot enough to make the pipe under the TRV much hotter than normal - just by heat conduction of the water in that short bit of pipe from return main pipe to TRV - assuming the hottest pipe with the lockshield valve on it is in fact the flow and not the return.
We then turned all the other rads back on and the rad in the kitchen cooled off quite quickly, as did the pipe under the TRV valve - though the pipe under the lockshield valve was still very hot.
Father in law says that the valve is working because you can hear the pump using scredriver, but I say this cannot be so because the rad cannot be heated from a cool pipe under the TRV and pass it to a return under the lockshield that is far hotter.
I examined all the other rads and in every case the flow (with TRV on top) is hotter than return pipe with lockshield on top.
The only exception to this is the new bedroom rad (fitted by the same blokes who did the kitchen rad) where the return + lockshield side is warmer than the flow + TRV side. This rad however does get very hot with no coldspots and I conclude that the TRV on this rad is of the newer 2 way type.
I conclude that the kitchen rad needs to have the valves switched round using an electric pipe freezer so that a drain of the entire system is not needed and that it would make good sense to replace the existing TRV with a new one that we know to be 2 way.
Would the above make sense to you or do you see a problem with my conclusion or indeed have anything to add that I may have missed.
At this stage I am discounting things like blocked pipes because the TRV pipe did get very hot (by conduction only IMHO) when it was the only rad switched on.