I believe you mean the beautiful and iconic Tower Bridge, not London Bridge which is rather ordinary.
https://www.towerbridge.org.uk/plan/
It is free to walk across it on the main level. The high walkway with glass floor does have an admission fee. If you walk there on the Thames Path on the south side of the river, you will cross under London Bridge in a wide passageway. There are colored lights set in the path and the walkway plays the music from the "London Bridge" song.
Big Ben is unfortunately silenced and the Tower in which it resides, the Elizabeth Tower, is covered for renovation, so you will not see that. But the Parliament buildings are lovely, especially from the south side of the river.
If it is a nice day, you can walk across Westminster Bridge from the Abbey area to the south side for a view, then turn left and follow the riverfront pedestrian path all the way to Tower Bridge. Lots to see along the way, including the London Eye, a skateboard park, an outdoor book sale, buskers at various spots, Shakespeare's Globe theater, St. Paul's Cross the river, the Golden Hinde replica, and lots of shops, restaurants, cafes, and pubs for break. It is a wonderful place to walk away from traffic. At Tower Bridge you can cross over to the Tower of London and see that from the outside, then catch the #15 bus back to Trafalgar Square. If you feel like turning back before going that far, cross on the Millennium pedestrian bridge by the Tate Modern, and you will arrive at St. Paul's and a stop for the #15 bus.