I am from Germany but I have lived here so long that I don't know the health system very well anymore. Generally I think the care is good but I don't know what you have to pay for.
In the UK, costs depend on two factors: whether you are self-funding (over £23,250 in assets) or not and in which borough you live, as they all charge completely differently for different things like day care, carers, sitters, respite and care homes. Your sister would be eligible for things like Attendance Allowance and council tax exemption, but I don't know how the system will treat people who have lived overseas for so long. You also might have to go through the process of getting diagnosed over here and getting into the NHS system and having needs assessments through Social Services.
The German state will be responsible for her care I assume as she has lived there so long and I find it strange that the POA (who is this person in relation to her?) wants to get rid of her instead of dealing with the care issue in Germany, and why he would contact you about it. You are in no way responsible for arranging anything and he shouldn't put this on you. If he thinks she might be better off here, he ought to organise it himself. But I would be very surprised if a country could just "deport" someone on the grounds of an illness.