London to St-Pancras

If you're flight arrives on time and the immigration queue is normal, then it should be enough. The easiest way is to take the Piccadilly line direct from Heathrow to Kings Cross/St Pancras. The ride from Heathrow will take about an hour. You need to be through the check-in gates for Eurostar at least 30 minutes prior to departure. It sounds like you already have bought your ticket, and if so whether or not it is enough time is largely irrelevant. Personally, I like to allow more time to accommodate a flight delay, but if all goes smoothly you will be fine.

I agree with Laura, generally. You don't say where you are arring from. Home? If so, an optomistic time to clear immigration, baggage reclaim and customs is 60 minutes. A pessimistic time is (if many planes arrive at the same time, or if there are immigration slow downs, or if the luggage is slow getting to the reclaim hall, or you get lost, etc.,) is 120 minutes. 20 minutes to find, get a ticket for, and board the Tube. You could be at one of several terminals and yu don't say which. 65 minutes on the Tube. 15 minutes to find the queue for Eurostar check-in, and move through the queue to the ticket reader and check in. As mentioned above, that ticket needs to be through the ticket reader 30 minutes prior to departure or you don't go. So:
9:40 + 2:00 (I'm a born pessimist with flying) + 20 + 1:05 + 15 = 13:20. OOPS. Missed it by 19 minutes. You needed to be checked in by 13:01. If everything is very fast at Heathrow, and you know exactly where your Tube train will be, and you borrowed an Oyster from a friend, and there were no delays along the way, and you booked it to the Eurostar check in and there was nobody ahead of you, you'd have time for lunch at St Pancras before you checked in. I couldn't say which it would be. I'd hope for the latter but be prepared for the former.

Thanks for the postings; in reply to a question, we will be arriving from the U.S. on United Airlines - that may indicate which concourse we would be coming in on and it's relation to the tube.

United uses two terminals at Heathrow. Flights from Newark and Houston fly into T4 (former Continental routes) The other flights (legacy United routes) come into T1. In either case, the tube is still the simplest transit option. Heathrow is well signed ... just follow the signs to the underground once you exit customs.

Bear in mind that the Heathrow Express train is the fastest way from Heathrow into London. It's nonstop and about 15 minutes to Paddington Station. You would need to take the Tube or a taxi across town to St Pancras. I've cabbed the other way, from the station to Paddington at 6pm on a weekday. It took about 45 minutes. Meanwhile, there's often a queue at Paddington's taxi line. The Tube from Paddington to St Pancras might easily be faster. If I had more than a carry on, I'd use a cab, though. I think your schedule is a bit tight. Booking a car to take you directly from Heathrow to St Pancras could be your best bet. Allow, say, 90 minutes for the trip. If you need to be in the queue at St Pancras at 1pm, then you'd need to leave Heathrow at by 11:30. That gives you, effectively, 90 minutes to get off the plane, traverse Heathrow, get bags, queue up at passport control, find your driver, and leave. That's possible. It's also subject to a lot of things causing delays. Your plane will be "on time" if it touches down at 9:40. But, it will take 10 minutes or so to taxi around Heathrow to your gate. Then, very likely, 10-20 more minutes to get off the plane, to your bags (big airport), plus more to get to passport control. (It's always taken me about 45 minutes to get through the Passport Control queue, once I got there. I allot an hour.)

Bear in mind that the Heathrow Express train is the fastest way from Heathrow into London. It's not if Paddington isn't your final destination. When you take into account the time it will to transfer from the Heathrow Express to the Tube, wait in line to purchase Tube tickets, and wait for the train to arrive, the Picadilly Line from Heathrow to Kings Cross/St Pancras is just as fast and much cheaper.