You can leave your luggage at the lesft luggage office at T4. It's £5.50 per 24 hours.

Another option to central London would be National Express coaches. Not sure how much it is but you can get more info from www.nationalexpress.co.uk

The Heathrow Express is the fastest but only takes you to Paddington, you then have to get a tube to wherever you wnat to go in London which is £4.00 on top.

You can get an underground 6 zone off peak travelcard for £6.00 which can be used all day after 9.30am. It's valid for all tube zones and covers the trip to and from Heathrow. That's probably the best value for a trip into central London.