Advice Extending Trip from Malvern UK to London

I'm currently in Malvern for a week-long cello camp and thinking about extending my trip to London afterwards. I'm not very familiar with the area and would love some advice on the best way to travel from Malvern to London. Should I take the train, or is driving a better option? Also, any recommendations on what to do in London for a first-time visitor would be greatly appreciated. Looking forward to your tips and suggestions!