Balti is definitely British.
Many claim the cooking style originated in Baltistan, but people familiar with Baltistan say no - most of the people there are vegetarians and balti is quite meat oriented - and the spicing is wrong.
Others report that balti is a Hindi word for bucket, so it might have been some Indian's joke about feeding the British out of buckets. In India the karahi (similar to a wok but more bowl shaped) is not brought to the table.