Thanks for your replies Guys,
It's obvious that this is not a common fault then! This is my 4th RX, and it's a new one on me. Right, answers:
1. Herbie - difficult to record as the noise is somewhat intermittent, but I'll have a go. Nothing to do with the door being open, exactly the same with the door closed
2. Zotto - it may well be the 'normal sound of brakes hydraulic circuit pressure charging', but it's a new one on me, and why didn't my local Lexus garage tell me that?
3. Barry - The start button has to be pressed for the noise to appear. And repeated pressing hard on the brake pedal when in Park can reproduce it, but the noise is still there when reversing out of my garage without touching the brake. Background is that I've owned the car for about 2 years, and the noise has always been there.
I have e mailed Lexus UK to ask if they have any comments or solutions. I do believe I am being fobbed off by Lexus Croydon, especially as the vehicle is under a comprehensive warranty.
Curing it is not essential and it seems to have no effect on the smooth running of the car. it's just an annoying noise that shouldn't be there, and may cause a problem when I eventually sell the car.
wbw - Peter