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If you're only in the city for a few days get a travel card. While it did save us a pocketful of cash the real benefit was not having to queue to use a ticket machine every time we wanted to make a journey. We picked up a tube map at the first station and off we went. Just bear in mind it’s much warmer on the tube than outside, so if traveling in the colder be prepared, you can find youself overdressed. Especially if you've got cases to carry.
The absolute best place to go if you're is Camden Market. It's absolutely packed with everything from 70s furniture to vintage clothing. It's on Saturday and Sunday. Get there early, get dinner in the food court, people watch, check out the barges on the canal. It's mental.
London is a very nice city, although very wet and rainy!!!