If you don't want to take your carry ons, there is left luggage. But putting stuff into store and retrieving it chews time (as well as cost) so unless you're carrying lead weights in your luggage I'd be tempted to keep it with me.
Head to the underground station within the terminal. Buy a "one day travelcard" for £12.10 per adult. That gives you unlimited use of all transport (except Heathrow Express, but that's not the problem it seems because that takes you to Paddington, which is not especially central).
Take the Piccadilly line, change (cross platform) at Hammersmith and step out at Westminster. You're standing under Big Ben, by the Thames. Start walking - just about all of London's famous sights are a short stroll or bus hop away.