BIA's RT Callsign was indeed "Britisland" with UK as the airline designator. When Air UK was formed, UK was still the airline designator and the RT callsign was "Ukay".
When BIA was resurrected after Air UK's failed attempt at the charter market as a separate charter outfit with BAC 1-11s and later MD83s it also used "Britisland"
Re Kestrel - this was dreamed up by a founder member Tom Beck (it was either going to be Kestrel or Nomad) - I was never sure if it was because of his love of ornithology or the fact that he had a Riley Kestrel car! Never liked it myself - the Spanish thought it was "Castrol". We had a bit of a reprieve when we went longhaul and "Tourjet" came along, but, as someone has already said, we had to revert to Kestrel as some minor Russian freight outfit had a similar sounding callsign and they had it first!