The remainder of the U.K., outside of London, has a larger dependency on the EU. These regions will suffer disproportionately more than London.

"In particular, Northern Ireland (the UK’s poorest region), the North East (England’s poorest region) and the South West (Southern England’s poorest region) appear to be the most dependent on the ability of the UK to trade in goods with relatively few restrictions with other EU countries." [1]

[1] "UK regions, the European Union and manufacturing exports" http://speri.dept.shef.ac.uk/wp-content/uploads/2016/05/Brie...