Is there a train from the port of Dover to Heathrow Airport?
If so, how much would a ticket cost? Also, if we have an extra day after landing in Dover, but would like to see something besides London, do you have any suggestions as to what we might visit?
The London Underground (subway system) extends to LHR, but the only overland trains are the Heathrow Express and the Heathrow Connect that run between the airport and Paddington station in central London.
However, thanks to the new high-speed service between Dover Priory and London St Pancras, you can get to LHR fairly quickly. (The trains run on the same high-speed tracks used by Eurostar trains going between London and either Paris or Brussels.)
Take a train from Dover Priory to St Pancras. Take a Piccadilly Line Tube (Underground) train from King's Cross/St Pancras to LHR. Your total travel time will be around 2 1/2 hours.
The 2nd class fare on the train from Dover to London is around 32 GBP. The fare on the Tube from London to LHR is 4.50 GBP.
There are lots of places that make for good day trips from London. What are your interests?
One caution is that Dover Priory station is some distance from the docks. There are regular bus services but most sources recommend at least an hour between docking time and your train.