(It's 'Caledonian Road' - it's generally not a good idea to abbreviate place names, you could end up getting it spectacularly wrong.)

If you buy a Zones 1+2 weekly ticket (which you can get at Heathrow Underground stations), and take the Underground (Piccadilly Line), then it will be at most £2.80 extra (and £1.50 for most of the day).
The London Underground does not have special add-on fares for airport services.

(There is an expensive, fast, train service - Heathrow Express - into London - but it wouldn't make things any easier for your journey.)