It should also be noted, for the non-Americans, that the Jim Crow laws often didn’t officially give blacks lower status. Most of them required “separate but equal” facilities (schools, businesses, etc.) for blacks and for whites, with the blatantly obvious fact that they weren’t equal being ignored by the local courts. And there were also things like requiring a literacy test before voting, where in practice a white would be given a very simple test (or the poll worker just waiving it), but blacks would be given much more difficult tests. Or a law that a person couldn’t vote without providing evidence that es grandparents voted (which of course was impossible, in the time of most black folks’ grandparents).
Not forgetting the laws that were in place in the North until the 1970s, which were designed to disenfranchise Catholics by basing ability to vote on factors such as home ownership, local authority tenancy, business ownership etc (with extra votes for people who met more than one of these criteria) and at the same time policies were in place to keep Catholics from meeting these requirements, eg local authorities would prioritise Protestants over Catholics for housing regardless of need. This didn’t quite rise to the level of Jim Crow laws, but it was part of a very deliberate policy to maintain Protestant supremacy.
I could be wrong, but even if you had a local authority home, I don’t think you could vote in the local elections, I think you had to own a property outright. The prioritising you describe sprang from the unfair voting rules but I don’t think it’s correct to say that the practice actually contributed to the voting unfairness, if that makes sense.
You have to remember that, as similar as places like London and New York seem in some ways now, the UK and the US had very different racial histories. The US used slavery of Africans on a widespread basis, the UK didn’t (it was actually banned for a period because it was deemed that England’s air was too ‘pure’ for a slave to breathe, unlike colonies like the US), which meant that in large swathes of the US there were huge numbers of black people, even comparable to the number of white people. That was never the case in the UK. Even up until WWII the black population in the UK was relatively small and confined to certain areas of big cities like London’s East End or near the docks in Bristol. It’s only in the last 60 years that really significant numbers of black people have immigrated to the UK from Africa and the Caribbean.
As a result there was never really any need for major discriminatory legislation - it was quite easy to discriminate against black people informally. They were refused service at shops and hotels, they were subject to abuse, and so on. But their numbers were small and they were largely confined in their own communities in large cities, so it wasn’t a ‘problem’ most Brits encountered.
You are wrong 
Local authority tenants could vote, this is precisely why unionist-dominated councils refused to give housing to nationalist families. CAIN refers to the tenant’s right to vote on this page (look under “Local Government (District Council) Elections”).
Ah, interesting, thanks for the link and clearing up my ignorance. My dad used to laugh about how he and his friends at Queen’s marched against Apartheid in the early '60s. They didn’t realise at the time they were living in a form of Apartheid.
I can’t recall any laws in the modern era aimed at “the Irish”. Legislation aimed at Roman Catholics would have done the necessary work in most cases.
After the Union there were examples of disparity in legislation between Ireland and the rest of the UK, of course. The franchise bar was raised to a higher level in Ireland, for example.
However, what one might call “general everyday discrimination” didn’t require positive legislation in the first place. Refusing to let a house to someone for the explicit reason that they were Black was perfectly legal until quite recently; not because there was a specific law either directly or indirectly allowing it, but simply because there was no law interfering with a person’s right to choose to do (or not do) business, etc. with whomsoever they pleased.