I had a distinct "whining" noise on my 2002 R53 Cooper S even when the steering was not being turned. The power steering pump then failed. I managed to get it replaced by Sytner Mini in Coventry as an act of goodwill for a cost of £265.00 inc. labour. It is a well known fault on Minis. In the USA they offered both a recall & 13 year warranty. In the UK should you experience a failure it will cost you. If the noise has just started, I would be concerned......