Here's an American video showing essentially the approach which I took, except he uses a much more expensive submersible pump and also uses vinegar instead of DS 3 as the descaling chemical.

https://youtu.be/8lw0iL7yBcA

Also Americans seem to have lovely service valves just below their boilers. These allow easy draining of the DHW heat exchanger and also easy pumping through of the descaling chemicals. See the video at 1:12. Can anyone point me in the direction of a similar type of valve to put on the domestic hot water pipes to my boiler? I reckon it would be worth a little bit of replumbing in order not to have to use the valves for the washing machine which are not exactly conveniently located.