According to the published official sources*, Michael left £5083 2s 3d to John Ll. Davies, and Rupert left £21,696 12s 2d to his elder brother Sir Thomas F Buxton.
*Principle Probate Registry
Calendar of grants of probate and letters of administation
I thought before that Michael was dependent on JMB for money, but as £5000 in 1921 would be worth about £250,000 now he had enough money to support himself, at least for a while.