Ginger - Whatever you DON't make a habit of arriving late!!
On the BA shuttle, it's probably a regular occurence (someone will correct me if I'm wrong.....!). But On alot of carriers (schedule and charter) you'll have two hopes of being allowed to go.... Bob and NO! It will screw up a departure (missing a dep slot or even sometimes a runway slot), mess with an on-time departure. Saying that anything upto 15 mins is classed as on time by the BAA.
My old company (Charter) if you're not at the gate 25mins before dep time, you & your bags will be off loaded and you wouldn't be going anywhere.
If you were going down to LHR to transit onwards (in other words you had baggage) i doubt you'd been allowed to make the flight.
But well done anyhow for getting down to get the flight.
All the Best - Mad-Air