rear wheel bearings whirring noise from 10mph+ Vauxhall Agila?

It is indeed quite possible that this is a tyre issue. However, if you jack a corner up (you don't need to jack both wheels at the same time) try rocking the wheel at top and bottom and at the sides, and give it a spin while listening carefully. Any untoward noises means further inspection is needed.

For what it's worth, my car does not like Dunlop tyres for some reason which no-one, including the makers, can discover. They wear in a peculiar stepped fashion and generate a noticeable drone on the road. This doesn't happen with any other make. It's a well-known phenomenon with this model.

Jack up both sides (one jack stand is all you need or a cinder block and some nerve). There would be no play with a bad rearwheel bearing but you would hear a big difference in the noise made but a bearing starting to go bad and compared to the other side which probably is still ok and a could control bearing.

The good news is a wheel bearing that is starting to make noise in not a big emergency they can usually hum along for quite some time - if you are only taking short trips.

Check your tires for flat spots and wear. Many vehicles have tires that are bad and they sound just like wheel bearings to an untrained person. If you have rear wheel drive and need both tires off the ground to spin a rear wheel you need to put the car up on a lift and run the motor with the transmission in gear to spin the wheels and listen to the bearing with a stethoscope. That way you know if they are making noise for sure.

Bad wheel bearings make a very deep sound. I would guess something dragging on the wheel, like brake pad/shoe. If it is bearings it is probably too late to lubricate that one. Spinning the wheel should prove fertile.

You have a wheel bearing gone, jack it up and spin the wheel, take 20 secs to diagnose that, failing that, find a mechanic

It's front wheel drive, isn't it? One rear wheel should spin freely. Or is it all wheel drive?

any noise freom any wheel bearings need renewed no quickies just get changed my advice for all drivers is join AA, RAC, AAA, OR GREEN FLAG, and when they attend watch and learn asked questions whether you are male or female,, know plenty girls and women who can repair cars..

Radial tires will make a terrible racket if they are not rotated so they roll the opposite direction every 6,000 miles.

It is your wheel bearing.