The most likely reason for a greater proportion of black and Asian people being infected than white people would be that a greater proportion of the former live in densely populated urban areas where the virus can more easily spread.
Which would have been a great answer if the graph from the ONS was showing infections, unfortunately it is showing deaths.
Those figures are also from early in the pandemic, when infection was mainly in a few large cities, again with a high minority population.
The UK population is very roughly split between 85% urban living and 15% rural living.
With the best will in the world, and whilst it may appear that some UK Cities have high BAME populations, I refuse to believe that any city in the UK has a BAME population that is 4 - 5 higher than a white population.
I'm afraid that your likely reason does not hold much water for me and there must be other reasons / factors for the numbers in the above ONS graph.