It makes perfect sense and is absolutely true. First, plug your transformer into the 220 volt outlet, then plug your "surge protector" (let's just call it a multi-plug strip) into the transformer, then plug your US appliances into the strip.
The only issue is how much load you put on the transformer. Say you have a 500 watt transformer and 4 appliances that each require 200 watts. If you were to plug all 4 of them into the multi-plug strip and turn them all on at once, creating an 800 watt load, you would overload the transformer and blow a fuse or worse. If you just turn one or two on at a time, no problem.
Check the rating of your transformer, and check the ratings of the devices you want to plug into it. It's simple math, just addition really. If your load is greater than your supply, either reduce load or increase supply (buy a bigger transformer).
Be aware that UK power is supplied at 50 Hz (cycles per second) and US appliances usually look for 60 Hz. This can be an issue for sensitive electronics, though they are usually protected by their own filters, or for electric motors which will tend to turn more slowly at 50Hz. I have not had any problems so far, and I run my US coffee maker, coffee bean roaster, and my wife's sewing machine through this setup and these are appliances not rated for 220 volt service. Remember to check ratings, if your appliance is rated for 220 don't run it through a transformer, just a plug adapter.
Word.
