I think you’re looking for long distance bridleway style stuff in England, and the closest would be the Pennine bridleway or the nearest approximation thereof.
I would look at train down to Peak district or even further south, then use the Tissington Trail and the southern leg of the PB to head further north/homewards.
The use of a cross bike suggests that you would be better travelling relatively light, rucksack at the most, so you could carry when needed, and hop on the road to join bits together.
I rode the PB route in the early 90’s from Hexham back to Manchester over 3 days, using Youth hostels and B&Bs, should be doable the other way…