Glad you agree. Yes, after the huge WW2 losses many thousands of Commonwealth immigrant workers came from the W.I. to fill jobs, at the NHS and London Transportand especially. Later Indian and Pakistani people took work in the mills up north, pls more Asians in the 70's from Amin's troubled Uganda.
The above period also saw higher emigration (e.g. 10 quid to Aussie), so that net UK migration was low until the 80's.
After that, immigration rose against migration and from the late 90's really took off to reach the hundreds of thousands net, (as below).
Below from: https://commonslibrary.parliament.uk/research-briefings/sn06077/