near the junction of the A14 and the A1 is a lovely riverside town of St Ives - not to be confused with the very popular town in Cornwall - with a very nice bakery (Tom's) who do tasty cakes.
On a more historic note, the (now pedestrian only) the bridge across the River Great Ouse was re-built in 1425 and incorporates a chapel midway across. https://en.wikipedia.org/wiki/StIvesBridge There is a working National Trust watermill just down the road and the Fens are nearby. Staying west of Cambridge a bigger town is Huntingdon. All this area was frequented by the diarist Samuel Pepys and so much remains 400 years later. A very pleasant area and town - I visit as often as I can. Not too far away, just south of Huntingdon, is another very pleasant riverside place, Godmanchester. Very scenic.
The problem is getting from that area, presumably by car, to Heathrow by just after lunch. Does that time include the return of the car?
There are three major car routes from the Cambridge, St Ives, Huntingdon area to the M25 London Orbital Motorway which circles greater London and leads to Heathrow.
The three routes from west to east are the M1 - reachable by the A428/A421 to Bedford and south; the A1 - passes through Huntingdon, very narrow lanes, many speed averaging cameras and low speeds before it finally turns into the A1M) many miles south; worst of all is the Black Cat Roundabout (also used by the A421) and in the process of being rebuilt with lots of lane closures, diversions and delays; and the M11 from Cambridge to East London - only two lane motorway and gives the longest exposure to the M25 and all its problems.
East Anglia is not well linked to the rest of the country.
I'd allow 2 plus hours for the drive to Heathrow on a good day.
For me, it would be too much stress before a flight.
If you don't have a car and can get from where you will be to a station at Cambridge, Huntingdon, St Neots (down the A1 from the A14) these all have trains into London Kings Cross station, figure an hour, and then tube or tube and Elizabeth Line to Heathrow, figure an hour for the tube or a bit less for the tube to Farringdon and the change to the Elizabeth line. No traffic and perhaps more reliable time prediction....