Eight Hour layover in London (London Heathrow)

You can catch the Heathrow Express into Paddington Station--a 15 minute ride. Then get on the underground to take you anywhere in London in just a few minutes.

For a rough guideline I flew into Heathrow T5 last Saturday, unfortunately because of the no fly zone over Iran we missed our planned slot of 05:35 which would have given us a headstart amongst the chaos of the flight arrivals post 06:02. The location of our stand required taking the shuttle two stops to arrivals (the shuttle was packed, our arrival coincided with the arrival of two other aircraft and it was bedlam).

At immigration we used the e-gates which took less than 10 minutes (assuming you're a US citizen you can also use the e-gates) and a further 15 minutes to walk to the luggage carousel and collect our luggage. If you have no luggage to collect then it's a quick walk through customs and head for the Heathrow Express.

You will need to be back at the airport at least 2 hours before your flight to Amsterdam. I have never experienced long delays at security at Heathrow although I'm almost always departing from Terminal 5. I would suggest that 30 minutes will be sufficient to get through security. There is no immigration process when departing the UK so once past security there will be no further checks other than your passport/boarding pass at the departure gate.

The best lounges are those provided by the airlines, I've used the Plaza Premium lounge at T4 before and wasn't impressed. Very busy, mediocre food and expensive for what it was. Access to the airline lounges are typically restricted to first or business class passengers travelling on the relevant airline or with associated frequent flyer status. I haven't used any of the airline lounges at T4.

The elephant in the room is the Sunday.

I don't think that using Heathrow Express and then getting onto the Circle line to Barbican which is the nearest tube stop to the Museum of London will be much better than using the Piccadilly Line to Holborn and changing to the Central Line to St Pauls which is nearly as close.

On Sundays most weekends the Circle line is partially closed due to the interminable Crossrail construction. Some weekends it is the northern half, some weekends the southern half, occasionally the eastern third. Yesterday it was the entire line.

Another possibility is Heathrow Express to Paddington, get onto the Bakerloo Line to the craziness that is Oxford Circus and change to the Central Line to St Pauls.

The museum opens at 10.

When you are done, do it all again in reverse.

Figure an hour each way on the tube.

If it is a domestic (within Europe) flight that you are catching in the evening, be back at Heathrow 2 hours ahead - 3 if going further.

A layover guide from TA:

https://www.tripadvisor.co.uk/Travel-g186338-c195392/London:United-Kingdom:Heathrow.Layover.Central.London.html

Thank you for all the advicee.. I has been helpful for guidance and some good tips.