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Took a trip to London summer before last, and only had a single focal length (35mm equiv) for the trip. It was great.
So, if you get a single and inexpensive fixed FL lens that is good, you won't spend much, you will get great pictures, and you will have time to consider whether to go longer, zoom, more fixed, or whatever. It'll be good in low light, good light, etc.
Consider a 35/2 or 50/1.8G and go from there. Keep it simple and cheap.
And if they don't work, I agree with Leighton, the 200-400 make a great walkaround. ;-)