Travel from Heathrow to Cambridge: options

Reality is no one can tell you how long immigration will take at Heathrow. It’s always a crap shoot and I say that after traveling to London since 1972. Most recent visit in 2022.

Take the bus. About 2 hours from LHR to Cambridge.

Taking the tube from Heathrow to Liverpool Street is not hard, a pre Elizabeth line task. One still useful to know for if routes via Paddington are experiencing problems.

Piccadilly to Barons Court, cross platform change to the District, then a same platform change to the Circle line at any central area station between Sloane Square and Tower Hill.

If the Elizabeth Line is having problems in the Central Core between Paddington and Liverpool Street, then change to the Central Line at Ealing Broadway, goes all the way to Liverpool Street.

The bus from Heathrow Terminal 2/3 to Cambridge is 2 hours 20 mins with no changes.
https://www.nationalexpress.com. Best if you want the driver to load luggage underneath and you can ride and rest. There are toilets on the bus. The bus is cheaper and better if you think you may have trouble with steps and/or carrying your luggage across platforms and navigating through people.

For Cambridge, you can use the following London stations: Thameslink services usually depart from London St Pancras International Station, Greater Anglia trains leave from London Liverpool Street, and Great Northern from London King's Cross station. There are two stations Cambridge and Cambridge North (you don't need Cambridge North it is 2 miles north of the city center).

https://www.thetrainline.com/ is a third-party site, easy to use and buy tickets. You can also buy tickets for an overground train service at the station kiosks. (Overground trains are not tap and go).

Alternatively, if you prefer a private driver you can have someone meet you in the arrival hall and drive you. You will need to prebook.
https://www.blackberrycars.com/ is recommended a lot but there are other companies out there.

Trainline adds surcharge to the fare you pay, so you pay more for the same ticket.

You can book the train tickets with the operating company, such as Great Northern, Thameslink and Greater Anglia.

The station is called Farringdon, not Farrington. That would only apply if you had come from Heathrow on the Elizabeth Line, not if you had come by tube on the Piccadilly Line- when you would transfer at Kings Cross/St Pancras.

The other tube station you could change to Thameslink at is Blackfriars- if you had changed on the tube to the District Line en route. That is an often suggested same platform change for Westminster and County Hall.
Blackfriars is quite a small station, so an easy change.

Traineline has a very minimal charge for booking. It is just a straightforward app to use when dealing with different train companies that may be unfamiliar to most outside the UK. This is why I suggest it and use it myself sometimes.