How does this work regards inheritance tax?
In theory, there isn't any. Although you do have to declare it in order for it to be tax-free.
After I pay inheritance tax in Poland, would there be any more to pay in UK?
In theory, as the money is tax-free income in Poland, under the Polish-British taxation treaty it isn't taxable in the UK. Although again you would want to get that confirmed in writing by the UK tax office in advance.
But, I'm not a tax adviser; you really
need to speak to a tax adviser.