Driving from London Heathrow to the Lake District

Chester is not far off your route, and it's a charming place with lots of good cafes and restaurants.

But I have a question. Are you just getting off a plane from the states and then planning to drive 5 1/2+ hours? I would really NOT recommend that. I was forced to do the same thing coming back from London recently and had to drive 2+ hours after a long flight, and I thought I was going to die. It's horrible; you're tired plus jet lagged (which are 2 separate things), and it can be dangerous. I stopped multiple times and if I had had any other choice, I would have rethought it.

I would seriously rethink this if you are indeed just getting off a flight from the states. If not, then see sentence no. 1 above. :-)

Re- the getting off a plane bit I agree. You are a serious hazard to yourself and everyone else on the road. I don't know how much time you think you will have but 5 1/2 hours is on the optimistic side. Chester may be an option but there is a very good reason why the City has Park and Ride buses.
Personally, except for Personal need breaks, I wouldn't be stopping until the Tickled Trout at Preston (the Blackburn exit), unless it had been a really bad day.
From the Trout there are several options.
Any regular user of the M6 has horror stories to tell, traffic wise.

Driving up is totally daft when the hourly train from Euston does the journey in under 3 hours. That will give you far more time to spare.

This is a potentially horrendous drive on some of the busiest and most frequently clogged-up motorways in the UK, through the heart of the industrial midlands.

Take any driving time estimates with a pinch of salt. I well remember the time a three-hour journey from the East Midlands to Manchester became seven hours because a lorry shed its load at Sandbach on the M6 on a Friday afternoon.

So you say you have lots of time: have you really?

I would choose the train from Euston any day of the week. I certainly wouldn’t do it if I’d flown in that day and was jet lagged - that would be extremely dangerous and negligent to other road users.

That said, if you’re not planning to do it straight off a flight, and for some reason you absolutely have to do it in a car, then maybe Knutsford (very pretty but expensive small town; I think the model for Mrs Gaskell’s Cranford) is close to the motorway just south of Manchester.

I'd echo but not repeat what others have said about driving for 5+ hours after a transatlantic flight.

You don't say what time you are landing, but I'd guess you'd need to allow for 1.5 to 2 hours from scheduled arrival time to clearing immigration, baggage reclaim and then getting to the rental area and actually getting behind the wheel - perhaps others can comment on this time estimate.

From this you can estimate how far north you will be by lunchtime (you can average about 65 miles in a hour on a motorway - Highway in UK speak - that's flowing) and look for a pub or small town near the motorway - try searching for something like 'country pubs near the M6'. The route you are most likely to take that goes up the M40 and then M6 has a number of attractive places close to a junction (intersection). I'd advise against speeding as most limits are now enforced by cameras and getting a ticket which you can't try to talk your way out of is a real pain in a hire car.

However, as a frequent driver of this route, I know that it can snarl up (once didn't move an inch on the M6 for 3 hours due to a severe accident ahead). If you have a good SatNav or can use Google Maps you may be directed by another route (eg M1 then M6) which is a few more miles but avoids a bad hold-up, so I wouldn't get too fixated on going to a specific location. If you leave the sound enabled on the SatNav or Google maps, it will tell you which lane to get in as you approach roundabouts (and you'll be seeing plenty of these) which is a big help if you are not familiar with roundabouts.

Even if the roads are clear that drive will be very tiring even without veering off route for stop. Driving in England is nothing like Texas. You may think a 5.5 hour drive is perfectly normal at home but it is anything but here.

If you are doing this straight off a flight from the US then I can't emphasise enough how bad an idea this is. Like Mardee I once found myself in the situation where I had to drive from Gatwick to Preston off a flight from Atlanta and it was truly horrible and I vowed then that I would never do it again. That was around 30 years ago and I haven't since.

If you are doing this after a few days in London and are using Heathrow to pick up a car then, as others have said, the train is a much better idea. By the time you set off from Heathrow having got out there, transferred to the car hire office and done all the paperwork you could be half way to the Lakes just watching the countryside whizz by. We have cars for hire in the north as well. Ask if you need any help with that.

I'm at Manchester Piccadilly rail station just now, which has 3 fast trains an hour from London Euston taking just over 2 hours. Although I use Piccadilly frequently (and have done all my life) I wasn't aware until I saw an inconspicous sign that Hertz have car rental at the station. So that is another possibility - train to Manchester, lunch and see a bit of another city, then rent from there.
From Pic you are more or less straight out onto Mancunian Way and the motorway system north.

Nothing wrong with your plan, so long as it is after a rest. Take the M25/M40 north to the M42/M5/M6. make sure you are not travelling in the rush hours, 0700-0930 and 1530-1830.
Just over half way in Cheshire is Knutsford which has already been mentioned, and there is also the smaller village of Lymm, about a mile off Junction 20.
Aim to get past Preston by 1600. If you leave Heathrow around 0930, you should be at Lymm by early afternoon. Have a bite and a mooch then get away before the evening rush.