Walking from Heathrow to hotels

If I'm not mistaken pedestrians are not allowed in the tunnel under the runway.

No walking route is available for the above reason.

There are hotels actually IN Heathrow that one can walk to. Terminal 3 has an Aerotel:

https://www.myaerotel.com/en-uk/find/americas-europe/united-kingdom/london/aerotel-london

We will be using the Sofitel in Terminal 5 on a trip next fall for an overnight layover there.

There are several more hotels connected to Terminal 4 by covered walkway, but I think T4 might be harder to reach from T3 than T5 is ( free transfer by Heathrow Express or, I think, by Elizabeth Line).

But if you prefer the Renaissance on Bath Road you will have to use some kind of shuttle system. I am sure others can advise you one that.

Call the hotel and ask them how they get guests over to Terminal 3:
tel:+44%2020-88976363%20

Make life simple. Take a taxi.

Most travelers take a taxi to one of the many hotels on the outskirts of the airport property.

I have used the Premier Inn at Terminal 4, a covered walk from the terminal. Free transfer from Terminal 3 by Underground via Hatton Cross or Elizabeth Line/Heathrow Express

There is also a Hilton Garden Inn connected to Terminal 2. You can get to it from Terminal 3 by an underground walkway.

Depending how much stuff you are carrying, don't forget the Red Bus option: 1.60 pounds or something - as far as you can go for 1 hour! Don't remember if anyone mentioned Hoppa buses. Sorry if they did, but they are cheaper than a taxi, and I am sure go there. I don't think you can walk anywhere from Terminal 3, but you CAN take free trains to any of the other Terminals: 4 and 5, but they are a long ways from that hotel by foot.