Is there a "standard" ratio of espresso to milk in a latte? If I order a caffè latte from a coffee shop, will it always be the same strength? As in the same ratio of espresso to milk? For example, I think I heard that Starbucks UK use more espresso than is normal, though I can't remember if that's compared to "normal for a latte" or the other Starbuckses in the rest of the world.

Or does it vary wildly from shop to shop (and thus I need to learn or ask at each individual coffee shop)?
It varies by shop and order.  For instance, order a latte at Starbucks, you have a selection of sizes, and then variance in the number of shots (or espresso) you order in the drink.  Since the sizes are not doubled (12, 16, 20 ounces, not 12, 24, 36) and half shots are not a thing, the ratio will vary at the order level.