Yep, layers are the way to go. The average high for June in London just creeps above 70 F by the end of the month and a half-rainy, half-sunny day is common. Of course, a heat wave could push things well into the 80s, but that's the exception, not the rule.
If you plan to do a lot of sightseeing, sandals may be more trouble than they're worth. Lots of concrete and cobblestone can lead to blisters without comfortable, broken-in walking shoes. Sandals for short outings are fine, but unless you've worn them while walking a few miles other than the beach, I wouldn't rely "solely" on them. Sorry, couldn't resist.