Well the room is toasty warm - for 3 days since the last intervention. Its still slow to heat up, and I know its not reaching its maximum temperature, but it will do.
Thank you all for your advice and suggestions, which have chipped away at this problem, and given a novice the confidence to tackle installing a rad, cutting copper, fitting compression joint, bleeding a pump and so on for the first time. It is immeasurably better than it was 4 weeks ago, and a lot of fun on the way.
TWgas - there is one spot where the plastic horizontal joins a copper vertical, which is inaccessible under the tiles. the copper rises 6 inches into the valve for the radiator. The next time I have the rad off ( and I know I will - its like picking a scab) , I will have a careful scratch around inside that copper rise with something long and pointy - see if there is some build up at that plastic elbow. Thanks for the idea.