Your 18-55 kit lens would be sufficient around London. It all depends on what type of pics you like to take.
Another alternative would be to dump your kit lens altogether, and buy a multi-purpose zoom that covers wide to telephoto, that you can walk around with all the time such as the.......
18-300mm from Sigma http://www.wexphotographic.com/sigma-18-300mm-f35-63-c-dc-macro-os-hsm-canon-fit-1560120/
or the 16-300mm from Tamron http://www.wexphotographic.com/tamron-16-300mm-f35-63-di-ii-vc-pzd-macro-lens-canon-fit-1553135/#1553135
As said before, these lenses will struggle in low light especially at the long end, so be prepared to up the ISO.
As Fodder said the Sigma 10-20mm is a great wide angle lens for landscape or getting lots in the frame.
Its all down to what you want really and how much you are prepared to spend.