UK National Rail search - expect at least £25 one way off peak after 9am and much higher before 8.30am. London-Bath will take 1.5hrs.
cheap flights are available to most European capitals for around £100 one way
London
travel on underground train system requires purchase of Oyster card which is an RFID smart card allowing you to touch on and off at each end of your trip with max. cost £7 per day for inner London travel. Can buy and top up at train stations and various outlets and can use cash, debit or credit card.