Things like phone chargers and similar tend to work with no problems — they'll recognise they're getting 230 V, 50 Hz instead of 115 V, 60 Hz and adjust themselves to give the correct output.

Of course, you'll need an adapter to put the dodgy American plug into the overbuilt UK socket, but more importantly check before you do this that the text on the charger says it's rated for 240 V. Because if it's not, it will probably mean that pretty soon you get to meet the local firemen.