Thank you very much for your reply.
My sister is very depressed and emotionally unstable at moment. I have already supported her over the 2 years. Although she tried to set up new life with someone, unfortantely no one would like to have long term relationship and marry her just because she has two kids. That is situation in China now.
Yes, she is happy if I can take care of them. There are 10 and 5 years old.
As they hold TaiWan's passport, they don't need the visas to enter to UK. I don't have enough money to pay them to go to private school here, I am wondering whether they eligible to go to state school.
They are living in TaiWan at moment.
I am British Citizen and I am Research Doctor working in UK.