Advice please!

I am wanting to fly With Virgin from LHR to Miami on a 11 am flight - next April. BUT I need to shuttle down from Manchester. BA do a shuttle that will get into LHR at 8.10 am. So my questions are, if I fly down business class to save waiting time, is 2 hours 50 mins long enough to get ofF the BA flight, collect luggage, change terminals and luggage drop for the Virgin Flight and clear security?

Ive tried to get both flights on one ticket but have been told by Virgin that they can’t do this.

I am thinking that the recommendation of arriving at the airport 2 hours before the flight isn’t mandatory and the check in desk doesn’t normally close until 1 hour before take off (I will check in on line so only need to bag drop).

any comments / suggestions appreciated, Katie’s Grandad - I need you !