Visiting Churchill's Chartwell Estate

You might find this link useful. https://visitbytrain.info/chartwell.htm
When the weather is good, the 2 mile walk from Westerham to Chartwell is a really pleasant way to reach the property. Look for the footpath signposted to Chartwell from near the top of the Green in the centre of Westerham. It's not far from the James Wolf Statue, but on the opposite side of the road. There are also several really good places to eat in Westerham. If you fancy an English tea room, then the Tudor Rose, on The Green is good, i also like Food for Thought, again on The Green
https://m.facebook.com/pages/Tudor-Rose-Restaurant/128023153913174
http://www.foodforthought.eu

Just found a couple of links to the walk from Westerham to Chartwell, which might be useful, should you decide to take in a bit of the kentish countryside.
http://www.visitwesterham.org.uk/visitors/v-walks-and-trails/v-other-walks
https://www.nationaltrust.org.uk/chartwell/trails/westerham-to-chartwell-trail

You might also like to visit Hever Castle as you're in the area. It was Anne Boleyn's childhood home and is nicely presented.

Taxis will be the easiest way to accomplish a visit to Chartwell and/or Hever Castle without a car of your own.

I visited Chartwell this past October, taking the train from London Charing Cross to Sevenoaks. There are taxis outside the train station. According to the Chartwell website, you can call from Chartwell for a taxi to return to the station; but because there were several reviews on TripAdvisor stating that warm hospitality and customer service were somewhat lacking among Chartwell staff, I arranged for a return pick-up with the taxi driver when he dropped me off at Chartwell.

My experience with the ticket staff at Chartwell? The young man was shockingly rude to me, to the point where he later sought me out to apologize, explaining that he had just returned from his lunch break when I collected my ticket. I guess it takes a few post-lunch minutes to gather one's cordiality.

Be aware -- the cost of taxi was around 40 pounds round trip.

The weather the day I was there was glorious, and I could have stayed far longer than the 3 hours I arranged! The house, the studio -- just fascinating; and the curators/guides were friendly, informative, and entertaining. Definitely a wonderful day out!!

There is a bus, but it only runs on Sundays and Bank Holidays once an hour.

Bus 246 starts back at Bromley, but you can pick it up from Hayes as well.

It is worth visiting. We had a rental car when we went and we also stopped at Igtham Mote on the same day.

The roses are gorgeous at Chartwell, even in the rain when we visited. Well worth the effort.