Folks,
(Preface: not an electrician... just some guy)
A number of my power tools are US running though a "big yellow box" and I've found few problems with it.
I'd recommend ordering a heavy duty US extension cord (one meant for a refrigerator or an air conditioner) then cut off the "male" end, replacing it with the goofy yellow "male" plug for the transformer.
All my "yellow" stuff came from ScrewFix, and the one yellow-to-US cord generally stays with the yellow box. I've a 3,000 watt permanently installed in the workshop and a little 750 watt I use for on-site work (mostly the small routers or sanders).
One word of warning... while the difference in US / UK frequency (60 vs. 50 cycles per second, respectively) may not be a big issue for speed, in many cases that difference results in the build-up of some additional heat.
This is not a problem for name-brand tools (I would die of exhaustion before my 110v Milwaukee Sawzall gave out), however it is good to pay attention to the "feel" of US tools when used over here. I've found it particularly true with sanders... both my 110v Bosch belt and RO get hot enough for me to notice, when used in anger, at which point I take a breather.
Also, if you're absolutely insane, you can get box of US power sockets (run back to a yellow box) and have duel power throughout your workshop. But that's just silly, right?
Thanks, Jim