A bit short (only 4 days) but the Herriot Way has hostels all the way round, YHA at Hawes, a yurt or bunkhouse in Keld and a YHA and an indy hostel within shouting distance of Reeth.
St Cuthbert's way has hostels at Kirk Yetholm and Wooler and I am pretty sure there's a bunkhouse at Beal, but you are stuck with a B&B in Jedborough.
If you want to take longer over the WHW, there is a bunkhouse in Drymen and SYHA at Rowerdennan which splits the stages up. The sticking point is the bunkhouse at Kingshouse being shut, but there are those hobbit houses at the ski place, and you can always get the bus (which is bookable, so they look out for you) back to Tyndrum or Crianlarich, or on to Glencoe where there are hostels. Then, as Bricam says, the Great Glen Way carries on from the WHW and is fairly well served with hostels.
The only thing with the West Highland Way is it gets quite busy and you have to book well in advance.