London
The EASIEST way to get from airport to Central London and back is by hiring a car in advance. The best company I’ve found to do that is Hummingbird Cars. Their website:
https://www.hummingbirdcars.co.uk/
There are also train options from every airport:
Heathrow Express: https://www.heathrowexpress.com/
Gatwick Express: https://www.gatwickexpress.com/
Stansted Express: https://www.stanstedexpress.com/
You can always take a bus into town. It’s the cheapest way to do it, but be warned: if there are accidents on the highway, or heavier-than-usual traffic, your journey could end up taking a LOT longer than you planned! National Express is, as the name implies, a national line that serves the whole country. They also have free wifi on all their buses!
National Express bus line: http://www.nationalexpress.com/home.aspx
Once you get into town, you’ll need to get around. Don’t bother renting a car: parking in the city is a nightmare, it’s very expensive (even if you can find it), and public transport in London is so good that you’d never need a car anyway! Buy an Oyster Card in advance (or at any London Underground [Tube] station): it’s the best way to pay for and use London Transport! (And Oyster Card is cheaper than those “Travelards” most tourists buy!)
Oyster Card info: https://tfl.gov.uk/travel-information/visiting-london/visitor-oyster-card
Peru
Machu Picchu: remember when traveling to high mountain areas, that the weather can change rapidly and dramatically. Even in summer in the Andes, be prepared for rain and cold weather: maybe even snow high up in the mountains! Layered clothing works best in the high Andes (or any mountain area, for that matter.)