Overnight Layover at Heathrow

There are many large chain hotels near Heathrow, not necessarily cheap, but served by the Hotel Hoppa bus that will take you to the various terminals. There's also the Yotel inside Terminal 4. If you stay in London near Paddington station, then the first Heathrow Express of the day gets to the airport about 5:00 a.m. most days of 5:30 Sundays; check train schedules for your terminal.

I'm going to suggest you stay by Heathrow. The only early morning option, besides a taxi, from London to Heathrow is the Heathrow Express. However, if three is a problem with the line, as there is occasionally, you are in deep trouble.

However, let's look at times:

Arrive LHR--5:25 PM

Immigration, baggage claims, customs--6:25

Get to Hotel, check in,--7:00

Train to London, taxi or tube to center of town--8:00 PM

There is a double decker bus tour called London by Night (there are actually a few that offer night tours). You might want to check out those. I doubt they pick up near the airport.

Check to see that latest train back to Heathrow.

If you are flying out of Terminal 5, I suggest you look into the Sofitel. While it is not the cheapest option it is connected to Terminal 5 via a covered walkway. Three minute walk to the terminal.

I'm with Frank on this. I really don't think getting into London is realistic.

A possibility that would give you some taste of England is staying a little off the airport. The last time I had an early morning flight from Heathrow we spent the night in the Premier Inn on the Bath Road and the evening before in the nearby White Horse.

https://www.google.co.uk/search?q=premier+inn+heathrow&ie=UTF-8&oe=UTF-8&hl=en-gb&client=safari

http://oldenglishpub.co.uk/

The pub was surprisingly local for where it is and we had a nice evening. I see that they now have accommodation so I would probably stay there, assuming it wasn't too expensive. You're close enough to the airport but not right on site.

There's a free shuttle along the Bath Road but I don't know if the timings would suit you.

Alan

The Sofitel could be the key for you if you want to get into London itself that evening. After immigration, take your bags and check in there, then immediately get the Heathrow Express from Terminal 5, less than 20 minutes to Paddington. From there you could take the tube to Trafalgar Square or some other central place and spend a couple of hours walking around looking at monuments and such, making sure you get back to Paddington (maybe by taxi?) before the last Heathrow Express leaves at 11:25. Then back to the Sofitel for enough sleep to survive the next day. Chances are your homebound flight will be leaving from Terminal 5, which is indeed a very short walk from the hotel.

You can buy relatively inexpensive advance Heathrow Express tickets online for a specified date (they don't require a specific time). And I got a Sofitel room last year for about $150 (nonrefundable) which I thought was a very good deal for such convenience.

Or follow the advice above about the nearby pub. Pubs are among the best parts of the UK.

My 2 cents. I did something similar a few years ago, flew in from LAX to Heathrow, around 4 pm, and had an early flight out the next day. We checked into the Sheraton located nearby the airport and took the Heathrow Express. We had dinner and saw sights.

We got back from London almost at midnight, and by the time we unwound from all the excitement it was time to get up.

If I may suggest, do NOT go into the city. It's actually not that closeby and at 5:25 you'll have most of the night gone.

Stay and check out the sites nearby. That way you'll be able to go to bed early and ready for your early flight out.

Thank you everyone, we booked a room at the Sofitel for convenience, so at least we will have the option to head into town if the timing works out. If not we will at least have a convenient room and can head to a nearby pub for dinner.

When you check into the Sofitel, let them explain how to find the room as the numbering is different than what you would expect.

I would chose one neighborhood or site to see and concentrate on that. So maybe Trafalgar Square, Soho, Piccadilly and have dinner somewhere nearby and then head back to the hotel.

Congratulations, as harry would say "CUBS WIN!"
Have fun.

what day of the week?

It is on a Sunday.