You will find a number of inexpensive ( in the scheme of things) mens outfitters that will pass muster with the types who frequent Canary Wharf in and around the Temple area of Fleet Street/Strand. These shops ( Stanley Ley/Ede and Ravenscroft etc) cater for the Bar and you will find excellent quality at a good price, they will also direct you to a local tailor who can hem your trousers.
As to shoes, Best value is Herrings ( online) they despatch to the US, otherwise just walk down Jermyn Street and go to Trickers/Grenson/C&Jones, get them to measure your feet and purchase accordingly.
If you are frequenting London then before you leave take one suit to the dry cleaners, pay in advance and tell them you will pick it up in a couple of weeks.