London 8:30 hour layover?

In a few days i will have a 8:30 hour layover in london where i need to change airports.
I arrive at Heathrow Airport at 7:40 and leave Stansted airport at 16:15.
We want to visit one waterstones and have lunch at an Honest burgers.
Is this possible? How can we do this in terms of public transportation? Is there another restaurant that is not super expensive that serves the impossible burger? (We want to try impossible/beyond burger)

If you are doing the journey between both by train, then there's an Honest Burger close to Liverpool Street Station where the train connects to Stansted.

There's a Waterstones close to Liverpool Street.

You can take the Underground (Subway) from Heathrow to Piccadilly Circus. The largest Waterstones shop in Londin is next to Piccadilly Circus Station. Then take a cab to Liverpool Street Station from which the Stansted Express trains depart and as another answerer says there's an Honest Burger place near Liverpool Street Station.
tfl.gov.uk
stanstedexpress.com

I'm sure this is enough time to do it even though the two airports are on opposite sides of London a long way apart. You could go to the Waterstone's at Trafalgar Square and I suggest that because it's a big one, and you can get there by Piccadilly line Underground from Heathrow to Piccadilly Circus, change to the Bakerloo line Southbound and it's one stop to Charing Cross. (We all call it the tube.)

But keep an eye on the clock and then go for lunch. 2 stops north on the Northern line from Charing Cross to Tottenham Court Road, Central line east to Liverpool Street, and there's an Honest Burger a short walk from there Eat and take the Stansted Express train from Liverpool Street - takes about an hour. I'm not suggesting taxis because London traffic then can be ruddy awful so I would "tube it".

Work out the timings first (the TfL Journey Planner will help) and plan your book browsing accordingly! Assuming you're coming from the USA or Canada, you could feel incredibly jet-lagged on arrival at Heathrow as 7:40 am there's 2.40 am Eastern Time, so you will want to sleep on the flight if you possibly can. See how zonked you feel on arrival and if you don't, there's a plan.

Being tall I can never even snooze in an economy seat so whenever I get home from "across the pond", getting home by bus afterwards (I live a few miles north of Heathrow) feels like an unreal experience. I immediately collapse into bed and sleep through the day, usually waking up in early afternoon.

Getting out of Heathrow isn't fast either. The line of bleary-eyed Americans at Heathrow at breakfast time has to be seen to be believed because so many flights go overnight, and I would bank on at least an hour to get through immigration and Customs. Of course as a British citizen I get to completely bypass it so I've never been through it.

So there's my idea of a plan, but be prepared to totally abandon it and just get yourself to Stansted.

Edit - thumbers down, explain why, or don't you have the courage of your convictions?

You'll need to find a burger place open that early (you'll need to find it for breakfast rather than lunch!)

But yes - you can travel into London, then back out to Stansted. Work backwards from when you need to be at the airport to plan timings and options; CityMapper is handy for planning routes