Plenty of people move to where the job is.
Moving costs money which people in poverty don't tend to have a lot of.
To rent a flat or house you need an admin fee for the credit check, the contracts, and the keys - typically a few hundred pounds. Presuming the credit check is passed you then need first and last month rent up front plus a month rent as a damage deposit. Based on a rent of £400 a month for a one bed flat that's £1200 before you can even move in. Then you need to move your furniture from A to B which again costs money.
Sign the child up for the local school at this new house and there's money for new uniform, their old one was blue but this new school is red. And there's no family nearby so you need childcare, 42 hours of childcare a week at £3.50 an hour is approx £580 a month, it's payable monthly in advance so the first lot of £580 needs to be paid to the childminder before you can drop your child off.
You don't qualify for free school meals now you're working and the school doesn't allow packed lunch. Dinners are £50 a month, payable in advance so that needs paying too.
Then you need to actually get to work. There's a bus every thirty minutes and a monthly pass is £90 which, again, needs paying in advance. And the council tax is due, £120 a month for a Band A property.
All that money needs to be paid before you even get a whiff of your first pay packet. Yes there's help in the form of housing benefit, council tax benefit, help a percentage of your childcare costs and so on but while you're waiting for those to be calculated and paid you have to pay it out of your own pocket which is impossible when those pockets are empty.
It's called the poverty trap for a reason.