Since they were landowners, it should be possible to trace them farther back, though the information might not be available online.
They had land around South Molton and in Loxbeare near Tiverton, about 15 miles away. They appear to have had the manor of Loxbeare since 1219, and still had it in 1420. I don't know how the two families or branches might be related. They had been there for 200 years, so the two families might be distant cousins.
There was a Robert son of William Avenel claiming land in Wykelegh (probably Withleigh) near Tiverton and Loxbeare in 1349. This wouldn't be the same Robert as mentioned before, since this one would have been born in or before 1328.
From Inquisitions Post Mortem (link below)
Warkleigh is a few miles from South Molton:
1/2 fee (in Warkleigh) which John Avenell holds, annual value 50s.;
John Avenell held to himself and his heirs the manor of Loxbeare of him by knight service, annual value nil except when the tenant dies.
From Common Pleas
Hilary (January) term 1425
Devon. John Avenell junior versus Alexander Loddenen or Loddeven, and others, for trespass: assault at Lokkesbeare.
Michaelmas term 1349
Devon. John de Puntyngdon versus Robert the son of William Avenel, for four messuages, 6 furlongs land in Wykelegh (probably Withleigh) near Tiverton, which Robert claims.
Inquisitions post mortem:
Feet of Fines