The whole premise of childcare for working mums relies on low paid (primarily female) workers. If childcare workers were paid more, mums of young children would not afford to use it and would find other solutions. Childcare would be affordable by a smaller section of society. Unless it's massively subsidised by the tax payer.
Childcare is a bad example really, it is badly paid but other than that it's rewarding, sociable hours , a pleasant working environment, relatively speaking. Hence plenty of British people are willing to do it, particularly young girls without many financial demands. There are plenty of horrible places to work that are staffed mainly immigrants - abattoirs, chicken factories etc.
The reason British people don't want low paid unpleasant jobs is that benefits are relatively high while steady availability of low paid workers keeps wages low. If people had no choice but to work they would be willing to do these unpopular jobs. On the flip side, there would be more poverty.
A high tax but more equal society is the only answer to this problem but that is not popular in this country.
Also you have to realise that incompetent people exist in every society. They don't become immigrants though. Immigrants are always going to be more hardworking and aspirational than average.