another great weekend trip recommendation: Hastings. It's about an hour and a half from Charing Cross Station and cost approximately 30£., and Hastings Station is only minutes away from the beach. Additionally Hastings has a stunning scenery to offer: From the ruins of Hastings Castle you have an amazing view over the sea, on clear days you can see miles along the coast.
In order to get to the caste you can either walk or take the cliff railway for 2.50£ (incl. return). The admission for the castle is 4.50£ and the view is quite nice. On the way back down the cliff you should make your way through the old town and stop for some lovely antique shops and some pasties in one of the cafes.