I am guessing that it will be approximately 15mins-1h35mins. (roughly)
Not directly, however you can get an East Coast Trains service to London Kings Cross and then simply take the Piccadilly line to one of the Heathrow Airport Underground stations (depending on which terminal you are departing from). Allow just over 4 hours for the journey.
Trains from York come in to London Kings Cross.
Take the Piccadilly underground (tube) line from Heathrow to Kings Cross and get the overground train to Ely from there. The whole journey should take about two hours thirty minutes.
Train to Kings Cross and then tube to Heathrow.
No. You need to get a Piccadilly line tube from any of Heathrow's terminals to Green Park, then you need to change onto a Victoria line train to Kings Cross/St. Pancras. From King's Cross train station you can get an East Coast main line train to Durham.
By underground tube train to Kings Cross Station.
Take the Piccadilly line from Heathrow to Kings Cross/St Pancras. From there you can either take a cab or continue on the Northern line for one stop to Angel station and it is then a five minute walk. If you decide to take 'the tube' all the way to Angel station, buy a through ticket at Heathrow.
take the pically line to kings cross st parncas and take thameslink from there
By road, use the M4, the M25 and the M1. By flying, catch a flight to East Midlands Airport and catch a bus to Leicester. The best way is to travel on the tube from the appropriate Heathrow Terminal sttion on the Piccadilly line then change at Kings Cross for St Pancras station which serves Leicester.
London (Kings Cross) to Luton is about 30 miles by road.
The Piccadilly line is the only one that serves Heathrow, so take it to Kings Cross and then change onto the Northern Line (southbound) to London Bridge Station.
4 Hours 30 Mins usually