I'm sorry op, please don't think all Brits are unwelcoming xenophobes. Most of the posts have been more constructive though.
Do come over here for a while, it sounds like you'd like the adventure and it's a good time with youngish children, and as long as you can get a good job, the standard of living is quite good compared to Warsaw (not sure about beyond as spent most time in the capital!).
I would be sure to have an exit strategy so you can always go back and not take a massive drop in standard living on your return.
And defo don't be a zero contract used and abused carer!!! There are good private (non agency) specialist carer jobs around, where you get paid better (£15 ph upwards depending on specialism), and treated better, so if you really want to go into caring, do that! Normally carers get exploited and it attracts people who can't get any other job, and are paid and treated appallingly... That's why we have repeated scandals about carers abusing their vulnerable clients. That's the state of the industry.
And also, of you're paid minimum wage (or shockingly, below), it's bloody hard to scrape by. That's when being here could become a trap. Don't believe everything you read in right wing media, it's not possible to have a good life subsisting on benefits and it would be an awful lot nicer to be living as you are now.
Anyway, I'd look at using your professional qualifications to get a job with better wages and hours. Is there a reason you said you don't want to look for something in that field?
Happy hunting, whatever you decide.