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.
http://www.visitlondon.com/things-to-do/sightseeing/london-attraction/big-ben/
Houses of Parliament and walk along the river towards Embankment.
https://tfl.gov.uk/modes/river/ to either Blackfriars for a look at the
http://www.tate.org.uk/visit/tate-modern
(£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/
and hop on a bus towards Liverpool street, see the City of London’s famous city
https://www.tripadvisor.co.uk/Restaurants-g186338-zfg9900-zfn7235727-London_England.html
http://www.whitechapelgallery.org/
and roads made famous by renowned criminals the Krays and earlier in time, Jack the ripper.
http://www.tate.org.uk/art/art-terms/y/young-british-artists-ybas