I used HEX in December on a trip to London. Buy tickets online. Here is the thread on coupon codes that will reduce your cost and save you the hassle of purchasing at Paddington. I was staying on the other side of Hyde Park, near the Queensway Station and actually walked from my hotel to Paddington, but being on the other side of the park, I'd be tempted to take a cab unless you have time to kill and it's a pretty day.

As a first-time visitor to London, I found the HEX-LHR combination pretty simple to use. Just to be absolutely certain and given that it's a Friday afternoon, I would allow myself one hour from the point of departure at Paddington to reach the point at LHR where you will reach the point of security clearance. Any surplus of time will be well spent in the Galleries Club World lounge.