For the route I echo what
@Ticktockmy and
@Tigerbiten advise. But you must set your route philosophy first, even before you choose east or west of Pennines eg:
Stay off trunk roads
Avoid (English?) A roads except when forced onto them
Follow NCN routes (or only when they don't wiggle)
Stay off minor minor roads (bends, gravel, cars coming the other way and can't be sure to pass, hilllier, steeper downhill, unknown bend at bottom)
Avoid climb ie by avoiding hillier lines or by seeking longer but gentler route choice (this has a macro and a micro application)
Wish to (seek out and) cross (and mostly climb) wilder areas, or not
Places (eg friends/relatives/'always wanted to visit') to go through.
A 'RidewithGPS' Soton > Edi'h gets you a route of 733km (not miles) so that suggests that, if you plan on 75 miles a day for 10 days you have a 60% extra route opportunity, so you have plenty of zig-zag room. In my comments below I'm working back from your detination.
@User9609 has offered his local (border) expertise. North of Carlisle/Banmpton, Eskdalemuir is pretty special heading towards Peebles but you also have the Liddesdale option up through Selkirk.
If you are taking a 'west' route (eg heading for Preston) then the bridge near Widnes is probably best for crossing the Mersey. There are forum members who can advise the best line through from Cheshire to Preston. Further north the Lune River valley NE of Lancaster right up to by Sedburgh is lovely, but you may want to go through the Lakes instead.
You're likely to wish to avoid the metropolis of Birmingham and its satellites so if you choose west then I'd head for Gloucester and then either head NW across to Leominster and up a LEJOG route through Shrewsbury, or stay a bit more north up the west side of the R Severn eg via Bridgnorth/Telford.
Out from Southampton, you could choose to go across the top of the New Forest to Salisbury and then there's a quiet road up the SW side of the Wylye valley to and through Warminster in which case crossing the Severn over the bridge is an iconic moment and opens up the options of the River Wye road past Tintern Abbey or over the Forest of Dean itself. Then there's an excellent line from Monmouth through Hereford to Leintwardine. Avoid the A49 which is the main N-S trunk road.