I often fly on separate tickets but I would never do it if I had checked bags to collect and re-check. It cuts a *lot* of your time out of the connection. If you don't have checked bags and do OLCI then as long as you get to the gate before they close the door you're probably ok. If you have bags to check you *must* be at the check-in desk before the bag cutoff or they won't take your bag. Not sure about Virgin but for the airline I'm familiar with at LHR the bag cutoff is 60 minutes. That's makes a huge difference.
Any way your friend can ship their bags ahead of them using one of the baggage shipping services? Maybe get the TA to pay for it?
Or just convince them that they don't really need checked bags -- Having traveled for a month to multiple climates in a single trip with a single carry-on I'm pretty convinced that except for sporting equipment and other such specialized needs there's really no reason to ever check bags.
Does your friend have the same situation on the way back? Note that at T3 the check-in desk is the only place they can stop you -- security will let you through no matter how tight your connection. But at T5 they check your boarding pass and if you aren't early enough by their standards they won't let you through no matter how able-bodied and how certain you are that you can get to the gate. It's one of the main reasons I'm leery about flying through T5.