lol@marina - we once won a prized in the school raffle for a sunday lunch at the clarendon, and remember the cabbage well.
Beety, we live 15 mins drive from blackheath, but will be here for most of the hols.
But how about trying Trinity College of Music or Greenwich University - both establishments are located in the Old Royal Naval College in Greenwich and as it's the holidays, it's very possible that they may rent out roooms as the students won't be there. Really good place to stay, not that far from Lewisham. And if you tell them the purpose of your trip they may be especially helpful.
Also, there's a place just next to Greenwich Station (not the Cutty Sark station- the other one) can't remember its name but it specialises in cheap but good accommodation aimed at students and backpackers - might be worth looking into. It's Called' St Christophers' I think.
Lastly, an actor friend of mine runs a very tasteful and slighty eccentric bed and breakfast in the middle of Greenwich. It's near the docklands railway - direct line to Lewisham. If you decide to b&b it, I can give him a ring.
Just had a look at the rock school website and am really interested. My oldest son would love it. I don't know if he has enough of a musical background to be eligible, and Easter may not be the best time for us, but I'm going to give the school a phone today
If you want me to do any research into accommodation, let me know.