www.tfl.gov.uk does routes for bikes (advanced search and only select bikes), that should give you the best way once your throught the foot tunnel (no cycling please!) and they have (or used to have) few maps that you could order with the cycle routes on, very handy and cheaper than an a-z
Oh and get some good locks.
www.tfl.gov.uk does routes for bikes (advanced search and only select bikes), that should give you the best way once your throught the foot tunnel (no cycling please!) and they have (or used to have) few maps that you could order with the cycle routes on, very handy and cheaper than an a-z