Somerset House lays on a couple of free guided tours every week, which are well worth doing.
This short one hour tour will show you some of the graceful staircases in the West Wing and the atmospheric Deadhouse, and introduce you to some of the Tudor intrigues that took place in the Strand mansion.
You'll also learn about about British naval power, see some interesting scientific curiosities, and get a taste of the extravagant entertainments laid on during the Georgian period.
If you're more interested in the personalities then you might like to try the Old Palace Tour of Somerset House instead, which concentrates on the building's Royal connections.
Old Palace Tour at Somerset House – Every Tue – The Old Palace Tour will introduce you to three Stuart queens who had an association with the old buildings at Somerset House
Skate! — Christmas ice rink at Somerset House – 14 Nov 2018 to 13 Jan 2019 – Somerset House has got the prettiest rink in London, with a huge Christmas tree and festive shopping arcade
Walk in the footsteps of Jack the Ripper – Every day – Walk the streets of Whitechapel and try and discover the identity of the Victorian murderer Jack the Ripper - if you dare!
The Original Tour — Open-top sightseeing bus – Every day – The Original Tour is one of London's most popular sightseeing buses, and it's also a great way to travel around the capital.
London Bus Tour — open-top sightseeing bus – Every day – This traditional open-top bus tour will take in all the best landmarks and attractions, with a free river cruise and guided walk.
TRS river cruise, from Big Ben to Greenwich – Every day – Spend a leisurely afternoon on a TRS river cruise from Big Ben to Greenwich, and see some of the sights along the river.
Boat trip down the Thames, with City Cruises – Every day – City Cruises offer one-way, return or all-day boat trips between Westminster and Greenwich, stopping off at Tower Bridge.
Look for more guided tours happening in October
Here are some more free events in London if you want a cheap day out
Disclaimer: Event details can change at short notice and you should reconfirm everything before making plans