Do bus and tube count?
I'm not thinking of specific journeys, but in general the sort of journeys you're talking about are likely to be:
stopping train - fast train - stopping train.
Split that fast train in london with two tube changes and you've got a lot of changes, for example
Aldrinton - Hove (all stations stopper)
Hove - London Bridge (relatively fast, no service past London Bridge due to Thameslink project)
London Bridge - Baker Street (Jubilee)
Baker Street - Paddington (Circle)
Paddington - Bristol (fast)
Bristol - Abbey Wood (stopper)
In this case you'd probaby just get the direct Hove - Abbey Wood instead, but I'm sure someone can find any equivilent route south - north that doesn't have an equivilent like that. Might be able to make it to 7 if you also need a change in the midlands between fast trains.