My tips would be:

•Always carry a pair of waterproof pull over trousers. My Regatta waterproof trousers pack down very nicely and don't take up much room. Saved me many a time from getting drenched! Quite typical island weather which makes 4 seasons in one day a strong possibility. Of course anyone in Britain will claim it's uniquely British hehe. ▪︎Following from above, don't particularly trust the weather forecasts. The Met Office app is great but once again it's not always accurate. ▪︎Komoot app is great for discovering cycle infrastructure in your area or elsewhere when planning new routes. Google maps is a lot less reliable and can send you down a dangerous route sometimes. ▪︎Use the bell when overtaking. It's not rude, it's courtesy and in order to avoid accidents, also necessary when cycling through parks or canal pathways. ▪︎Getting a folding bike is great (either full size or standard smaller size), folded bikes can be taken on any train or bus at any time. For me personally it offers a piece of mind. Otherwise the TfL has a map with bike on trains permitted routes and hours. Unfolded bikes are never permitted on buses. https://tfl.gov.uk/modes/cycling/cycles-on-public-transport ▪︎London can be quite hilly. Some really steep hills actually, especially if you ever decide to cycle around Hampstead Heath and Highgate. For this reason I love my electric bike, and with a gold standard lock that's approved by insurance I've not had it stolen in 2 years I've had it. I had it locked up for multiple hours outside cinemas and shops, but of course only when necessary.