Most motorized appliances will work on only 120V or only 240V and are not switchable.
You can use a step-down transformer to convert 240V to 120V for most smaller items, such as blenders and mixers, but you'd need to weigh the cost and inconvenience of using a transformer against that of buying U.K. replacements.
The other problem with respect to motors is that it's not just the voltage which is different in the U.K. but also the supply frequency -- 50 Hertz (cycles per second) here vs. 60Hz in America. The smaller motors in blenders etc. don't have much of a problem with the difference, but it can become much more significant as the motor size increases, and can result in poor efficiency and overheating on larger motors such as those in heavy-duty vacuum cleaners, fridges, and washers.
Unfortunately, a transformer converts only the voltage, not the frequency, and although there are ways of carrying out frequency conversion, it's a much more complex process.
Even if your cleaner will run on 50Hz adequately, if it's a heavy-duty model you'd need a hefty transformer to step-down the voltage. All things considered, you'd be better off buying a replacement over here.