London is an amazing city, I am currently living here and am never bored. Although the weather can be quite miserable, it's a well-known thing and to come here expecting a week straight of Sun would only mean you'll be disappointed. There's an abundance of things to do in London and the tubes make everything so incredibly accessible. Everyone needs to see London!
Insider Tip:Contrary to what you might think, being a major city, London does not have 24hr transport (bar a few bus services) so make sure you check when the last train is and where it's last stop is!! Trains also don't run early Sunday mornings.