Heathrow Express to Paddington 15 mins, Paddington to Liv St 20 mins. It takes an age just to walk between Piccadilly and Central lines at Holborn the prospect of which, with a suitcase, laptop bag and duty free goody bag didn't appeal much to me at 530am this morning . The tube journey from Heathrow to Holborn also takes an eternity. I'll take the extra 15 pounds for the comfort (and if things run smoothly) massive time saving thanks
In reality it takes nearly twice that time, as you found out, which is what makes it often quicker to do by tube where services are more frequent on both lines.