I will be arriving at London Heathrow Terminal 1 at 5:55am. I want to book a train connection but I am not sure how long to allow for going through baggage claim then customs/passport.
Unless there are lines, which cannot be predicted, immigrations is a brief stop and stamp, customs is a walk through. No more than 30 minutes from the time you exit the plane. It will take you much longer to get to the train station.
I disagree with Frank. Arriving early in the morning at Heathrow, you can certainly predict lines at immigration, as that's when LOTS of trans-Atlantic flights arrive. I don't know how long to allow, but 30 minutes for the whole process would be very optimistic. The last time I was at Heathrow was years ago, but the immigration line took almost an hour (and this was before 9/11/2001). The line moved at a good clip, but so many other flights had landed at the same time, so the line was immense. And yes, you go through passport control (immigration) first, then pick up your checked bags, then go through customs (usually a walk through the "Green Channel - Nothing To Declare" line, unless you are stopped for inspection or have something to declare).
A few years ago (7 or 8) it took me an hour or more to pass thru passport control at Heathrow. The past few years, the early morning procedure has been under 30 minutes for me. Baggage claim comes after passport control.
That's really a loaded question. The immigration queues at Heathrow can be legendary and a constant source of complaint locally. As someone who has used LHR quite a bit, I typically plan for an hour from the time I step off the airplane until I am through the baggage area. I've done it in far less time, and been stuck for a lot longer. My average is about 45 minutes. Plan for an hour from off the airplane to through immigration and baggage claim and exited the secure area.
The plane lands, then it takes a while to get off (10-15 min), then there is a long hike to Immigration (passport control), the you stand in line for a few seconds, minutes, or longer. Next is baggage claim (if you checked yours), then you walk thru the door "nothing to declare," if that is appropriate, then walk to exit. It can be done in less than an hour if there is no long line and passport control doesn't decide to pull you aside for special treatment. I've also had this process take two hours, most of that time standing in line at passport control. When several planes land around the same time, it can take longer. The only "shortcut" I've figured out is to wait until after passport control to use the loo. This gets me in line ahead of the people who stop along the way to use the facilities.
Which sort of train do you want to book? There aren't any trains from Heathrow which require booking, only the Heathrow Express and Heathrow Connect go from Heathrow, and the Underground - none of which require booking. If you are planning on taking a long distance train from somewhere in London you will need to factor in several other issues.
To give more detail, the flight arrives @ 5:55am on June 25th, 2013. After going through passport/customs/baggage claim Iwe are planning on taking Heathrow Connect to Hayes & Harlington. I am wantingto book the train from Hayes & Harlington to Exeter. So, with all the factors, I am trying to figure how much time I will be spending once I arrive @ 5:55 before I can catch the Heathrow connect which runs every 30 minutes.
Scott, your question has been answered as nearly as possible. The answer: it depends!
Hayes and Harlington is an inconvenient exchange point for trains to the South West. You would be better off going all the way into London - or catch the Railair Coach to Reading (if you went to Hayes you would have to catch the slow train to Reading anyway).
Figure on a reasonable day to pass through the frosted glass doors around 7am; 7:30 on a slower day, so Paddington by 8:30 to be safe? There's a 7:30 train to Exeter from Paddington but I see no reasonable chance of you making that one. The 9:06 is the next choice, and that seems like a goo choice to me. It takes 2:16 and arrives at Exeter at 11:22. Tickets purchased well in advance (or later if there are still tickets available, they are quota controlled) can be had for £25.50, calling at only 4 stations on the way.