Any parts of London that have a “village” feel?

For anything resembling a village you will have to get out of central London but there are options. Wimbledon village could be combined with a visit to the tennis museum (there's even a windmill, on Wimbledon Common), BlCkheath could be combined with a trip to Greenwich. Go to Hampton Court and extend into East Mosley.
Check out Battersea Park for children's palygrounds, there's a High Ropes course (chargeable) in addition to the free attractions.

What do you want from a village? I live in a village a few miles from Tunbridge Wells in Kent. It has a small post office, a cafe, a pub and a butchers and a few swings and a slide for young children. Most children visiting here would be bored rigid. In the adjacent village, the village shop and pub have closed over the past 5 years, so it has no facilities. Yes, the local architecture is attractive and we are surrounded by glorious countryside, but you need a car to explore it.

You aren’t going to get village life in London - there are too many people and far too much traffic. There are some places that don’t feel like a huge city, such as Highgate, Richmond, Hampstead or Chiswick, but they don’t feel like villages. You need to get away from the major trunk roads for the “village” feel, but this means being further from public transport facilities.

The London Transport Museum in Covent Garden is interesting for children if you haven’t been before.

I would think of Hampstead as having a village-y feel (shorter brick buildings, very pedestrian friendly, etc).

I bet there are a ton of articles from travel publications and newspapers on “London for kids” that might mention fun parks etc.

My grandchildren loved the playground in St. James Park, with climbing opportunities and an interesting swing, plus rocks and sand. The birds ( mostly waterfowl) in the park are a bonus.

We did not make it to the Princess Diana Memorial Playground in Kensington Gardens, but it is also very popular.

I see these two playgrounds in particular are recommended in this article, with photos:

https://exploringthroughlife.com/two-london-playgrounds-not-to-miss-with-kids/

What about that area on the north side that has the canals and houseboats? I'm sorry I cant come up with the name.

distaver, you might get better results if you added your hometown to your visible profile, as have most of the responders so far. If you're from a rural area, we might understand your wishes better. Like most big cities of the world, London requires extensive transit usage to see "things". But like my own hometown, New York City, people who live in a flat don't use their car to buy everyday things - they shop and even dine in a walking radius. In that way, I say that NYC is a collection of neighborhoods.

I don't think you were referring to "old" architecture, but there's plenty of that all over London. Do you mean "a playground or park, and a convenience store to stock our self-catering kitchen within walking distance?" There are neighborhoods all over London like that.

I have to say, even when we rented in the Lake District 25 years ago, big-box supermarkets were already driving the village specialist markets out of business, especially with the decrease in free time for parents. We were able to walk around town with a basket on our arm, but it was the last gasp of an era.

There are areas of Blackheath, Kew, Richmond, Highgate, Hamstead, and quite a few other suburbs that have a "village" atmosphere once you get away from main roads.

LondonWalks has tours of both Hampstead and Highgate. I found both worthwhile, but I thought Hampstead was visually more attractive. The Highgate tour is rather hilly. The company's walking tours are just-show-up affairs, so you can keep and eye on the weather and seize a good opportunity for an informative, entertaining 2 hours.

Stan: the name you're looking for is Little Venice, and its wonderful. So is Hampstead.

Thanks for all the responses, they've given me lots of ideas to research. Very much appreciated!!!

Depending on how long you've got you could consider going to Richmond. On your left as you come out of the train/tube station and behind the main street is Richmond Green which is a pleasant green square with trees, nice pub overlooking it, and a couple of excellent ice cream parlours down the cute alleyway leading to it. From there you can meander down to the River Thames. Turn left and it's a really nice walk in the meadows by the river to Petersham where there are very pretty woods, and, if you feel like it there's a little passenger ferry that you have to shout for if it's on the wrong side of the river to take you across to a playground. Come back over to the Petersham side and you might catch the posh people playing polo or you could visit Petersham Nurseries which has quite a villagey feel and a rather pricey cafe/restaurant. If you still have energy you could make your way up the hill to have a look at the view or to go into Richmond Park where you get a real countryside feel and there are a lot of deer around. Richmond is also well placed for going to Hampton Court or Kew Gardens, if you were interested in them.

If you don't have time for that then wandering round Hampstead is great too - go down Flask Walk and get lost in the back streets around Burgh House and then up to the Heath is nice.

We stayed within walking distance of Richmond for 2 weeks and I agree with many here that Richmond, near the green and Thames would give you a charming center. There are green areas, playgrounds, Kew Botanical Garden, shops, historic homes, Thames path walks. We took one walk along the Thames from Richmond to Twickenham to see Eel Pie Island. There were playgrounds and pubs along the way. I loved Richmond. it was easy to get to central London, Hampton Court Palace and the airport.

EDIT: We had our, then, 8 year old granddaughter with us. She loved the walks and playgrounds near Richmond and the Thames. She said she’d tell her parents that she had her first pint at a pub with us 😉 at one charming stop. It was a pint of peel and eat shrimp so we said go ahead and tell your parents!

I appreciate both of your responses, we can't wait to visit these wonderful places! Thank you for the suggestions!