Anyway I would suggest Sweden, Netherlands, Australia, New Zealand, Canada, Switzerland, Austria, Ireland, Germany, France, Japan, even the good ol' USA for starters. Statistically proven people seem to be happier (but maybe thats just the British/English disease) their education systems arearguably better (eg Our European counterparts learn foreign languages yet we can't even be bothered as a rule to learn theirs. Although you will say that English is the primary global language so its a necessity) as health care (albeit not the USA)
And one can certainly pick criticisms in these countries too...
Some of those countries did take our legal system, others didn't. As for our railway system...well England invented football and cricket but they're hardly the best at it now! As per the NAtional health service.
Again I apologise wholeheartedly for the HIV jibe.