In 1945, when Australian, Canadian and NZ troops helped complete the liberation of Europe from fascism, people from all three of those countries had the full right to settle in the UK. They were all British subjects. Then time moved on and Europe decided to heal itself by forming the EC and since then has engaged in beggar-my-neighbour economic policies through farming subsidies. This has done great harm to the economies of the aforementioned countries, Aus and NZ particularly once the UK entered. Until then, those countries exported huge amounts of foodstuffs to the UK, meat particularly. There is absolutely no reason why that can't be reinstated.
Now, only after Brexit, the EU has come sniffing around for a trade deal after 30 years of non. I don't think that's any sort of a coincidence. I would like to think that it's a belated recognition of the debt that the countries of the EU owe, but I don't think so somehow.
There is also no reason why FOM shouldn't be reinstated. Those countries were shut out in favour of EU nations. It may be sad for the people of those countries if the pendulum were to swing back, but it would be no worse for them than it was for Aus / Can / NZ.
Someone above said there were no links worth preserving because they were based on colonialism. This is pure snobbery, and ignores the fact that there are actual family relations involved. Where I live, most people have a UK grandparent or great-grandparent in the mix. The cultures really are similar, and the benefits of migration for both countries very real.
As for racism: all three countries have absorbed far more immigration per capita than the UK without anything like the tensions the UK has, and frankly there is very little the UK can teach them about race relations. Yes of course there is racism, but it's a very common mistake for UK immigrants to confuse a simple lack of politesse that exists here with the sort of racism that an awful lot of people in the UK simply keep quiet about.
I grew up in England and now live in NZ. I got far more racists crap in Scotland. In terms of race relations, there is a far more honest, straightforward and long-standing dialogue not to mention progress about these things in this country and it really does compare favourably to the empty rhetoric, hypocracy, grandstanding and hypersensitivity that characterises the UK's relatively weaker efforts on the same topic.