Hello! It sounds like you are planning an exciting trip to London, Cardiff, and Edinburgh. I'd be happy to provide you with some travel information.

Best Time to Visit:
The best time to visit these cities in the UK is during the late spring (late April to June) when the temperatures are mild and the parks are green. The early fall (September to October) also offers pleasant temperatures and smaller crowds.

Route and Accessibility:
All three cities are well-connected by train via the UK's extensive rail network. From London, you can take a train to Cardiff which usually lasts about 2 hours. From Cardiff, you can then take a train to Edinburgh which takes around 7 hours. Alternatively, flying between these cities is another feasible option.

Accommodation and Booking:
These cities offer a wide range of accommodations to suit all budgets - from luxury hotels to hostels and vacation rental apartments. It's best to book your accommodations in advance, especially during the peak tourist seasons, via reputable online booking platforms or directly through hotel websites.

Clothing and Essentials:
Weather in the UK can be unpredictable, so it's a good idea to bring a waterproof jacket or an umbrella. Layers are the key, as well as comfortable walking shoes for sightseeing. Don't forget your travel adapter for UK power outlets.

Health and Safety:
The UK is generally safe, but as anywhere else, remain aware of your surroundings, especially in crowded tourist areas. If you have specific medical needs, ensure that you have an adequate supply of medications, as well as travel insurance that covers health.

Local Etiquette and Respect:
The British are known for their politeness and good manners. Remember to say please and thank you. When in crowded places, like public transport, it's considered polite to keep noise to a minimum. In pubs, it's customary to take turns buying rounds of drinks.