Hello all! I hope this is the right place to post such a question!

I live in Southern California. It doesn’t get ‘real’ cold here. However there’s a 95% chance we will be going to London for work the end of January next year for a bit over a week. I’ve looked at the average weather for that time of year and it’s coooold! Lows of mid 20s, highs of mid 40s. I’ve also been advised it will probably be rainy.

I have a 3yo who lives in tees and sneakers. He is not prepared for this, wardrobe wise.

I don’t want to spend a ton on things for him because honestly he’ll only use them this time and never again so I have no issue going consignment but my question is what do I get?? I snagged a puffer jacket on super sale but past that I don’t know. What type of shoes should he wear? Snow boots? Rain boots? All weather boots (like Timberlands - I’m not sure what their official name is). Also, would jeans with some thermals underneath work okay? We will be traveling and sightseeing about half the time and only taking the tube so I want him to be warm. I’d love any advice from London parents, or just parents who live in cold weather. Thank you!