The best way to travel to London from Brighton is by train. http://www.southernrailway.com/tickets-and-fares/ticket-types/travelcards/ –
get a travel card zones 1-6 from your local railway station. This allows you to hop on and off the buses https://tfl.gov.uk/maps/and tubes and get nearly all the trains there and back to Brighton.
From Brighton station, take the train to Victoria and get off the train onto the tube to Westminster to see the sights.
1. Big Ben
Houses of Parliament and walk along the river towards Embankment.
2. Jump on a riverboat
https://tfl.gov.uk/modes/river/ to either Blackfriars for a look at the
3. Tate Modern art gallery,
4. Borough food market
5. Take a cruise
(£3.50 with a travel card) to St Katherines dock to see the Tower of London and Tower Bridge. https://tfl.gov.uk/modes/river/
6. Jump off the boat
and hop on a bus towards Liverpool street, see the City of London’s famous city
London East End Markets
7. Jump off the bus at Spitalfields market
8. Stop for a coffee in one of the many cafes there.
9. Feel the atmosphere where old London and new London meet, the curry houses of Brick Lane, WhiteChapel Art Gallery
and roads made famous by renowned criminals the Krays and earlier in time, Jack the ripper.
10. See how famous YBA have made
11. The east end fashionable and have a coffee and watch all the hipsters go about their day.