Sure, I'd be happy to provide you with some travel tips for your visit to London, Liverpool and Manchester.

Best Time to Visit:
The best time to visit these cities is in the late spring (April to June), when the temperatures are relatively mild and the parks are green and blooming. September to November is also a good time to visit as the summer crowds will have gone but the weather is still pleasant.

Route and Accessibility:
All three cities have international airports and are major hubs for train and bus services in the UK. In London, you can use the London Tube and double-decker buses for getting around, while in Liverpool and Manchester, local buses and trams are available.

Accommodation and Booking:
There's a wealth of accommodation options in these cities from luxury hotels to budget hostels. Booking online in advance on websites like Booking.com, Airbnb, and Expedia can help ensure you get the best prices and availability.

Clothing and Essentials:
Packing a lightweight waterproof jacket and an umbrella is almost a must, given the UK's unpredictable weather. Comfortable walking shoes are also recommended as these cities are best explored on foot. If visiting in winter, ensure to bring warm clothing.

Health and Safety:
The UK is generally safe to travel to, but like anywhere, usual travel care should be taken to protect belongings and personal safety. Emergency services are available 24/7 by dialing 999. Ensure your travel insurance is up-to-date before travelling.

Local Etiquette and Respect:
British people value manners and respect. When using public transport, remember to stand on the right side on escalators, let people off the tube or tram before boarding, and queue in an orderly manner.