In reply to DanForsh:
In a really good freeze, sourmilk gill, Buttermere gives 1000 feet of easy angled ice, follow it up with one of the descent gullies on chapel crags then a stroll along the tops to scarth gap and back along the Lakeshore to the village.
Or more cynically, any of the trade route low level ice falls (launchy etc) will be possible with 1 axe, once word gets out they are mobbed and so stepped out you can get by without an axe.