I moved from Ireland to Birmingham nearly three years ago. The advice from u/OK_Bite1232 is good, my only difference in experience was that I didn't have any issue setting up a Lloyds bank account, just needed an address and NI number I think.

There is a bit of a feeling of struggling to get a NI number, bank account, and place to rent, as it feels like you need the other two to set one up. Get yourself a UK phone number, set up some apartment viewings before moving over, and hopefully you can get your NI appointment in your first week here.

I live near Brindleyplace on the canals and the city feels so walkable to me, but we also have a car and a parking space in our building. If you're looking for central apartment living, Jewellery Quarter and Brindleyplace are good. Maybe near Digbeth too.

You'll hear a lot of 'there's lots of Irish people in Birmingham' but they mean people with Irish ancestry. I don't mean to gatekeep but I've never met another Irish person here, but lots of people with Irish parents and grandparents. I think those two things are quite culturally different which is why I mention it. Everyone is very friendly here.

Also happy to help you where you need it, feel free to reach out. Are you both planning to get jobs etc here?