It is quite possible from a electrical point of view to install a large transformer and run 120V to NEMA outlets. I have precisely this arrangement to run all my 120V technical equipment.
To do this for high-power kitchen appliances, however, is unlikely to be a viable proposition. Big transformers are expensive, and by the time you add the labor costs you could probably have bought at least a new washer and dryer over here.
Also to consider is that it is not just the voltages which are different, but also the supply frequency (60Hz U.S., 50Hz U.K.). This isn't generally a problem for small motors (electric carving knife, can opener, etc.) but when you start getting to the larger motors in washers and refrigerators, it can become more significant and result in the motors running less efficiently. I wouldn't recommend it. (Yes, frequency converters are available too, but you really don't want to see the price tag for one big enough to run this lot!
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You'd also have a hard time finding a British electrician who would be willing to do the work, as most are not familiar with American electrical standards and will not install anything outside the standard to which U.K. wiring is normally carried out anyway, although there is no law against it. (If you were renting a house, I doubt whether the landlord would be happy with the idea either.)
The dryer would also need special wiring, as American dryers have a 3- or 4-wire hookup and run on both 120 and 240V power. They also use different grounding (earthing) arrangements, so there would be added complications with which, again, many U.K. electricians would not be familiar.
My advice on the fridge, washer, and dryer is to forget it and buy replacements over here, for both technical reasons and the practicalities (size etc.) mentioned by others.
If you really have a lot of lower-power gadgets you're attached to, then installing 120V power for those is more practical, although still likely to be more expensive than buying 240V replacements over here.