My favourite time of the year especially when I have to go into the city. ^
June can be very pleasant most of the time with many sunny days much like Spring time in London and excellent for walking about. If the wind swings round to the south it can be chilly especially if it's overcast but nothing really too unpleasant.
Just bring a wooly jumper and a jacket as it does get chilly at night.
June = No mosquito.......hooray.