I've never known Farnborough object to any routing 'straight line' anywhere unless it passes through the Odiham ATZ rather than above it. I often plan Popham - Hook - (across Odiham ATZ) - Petersfield - B Waltham -(across Solent E-W) - Romsey to Old Sarum for a navex for US or SA trained pilots wanting to start flying at Popham and new to UK airspace. Looks horrendous, works fine.
The think about Solent is to notice the orientation of airspace, which suggests N-S routing would be unwelcome, (due to runway alignment), (so route to one side), whereas E-W OK unless your radio patter is - err- um --err ---- err -- quite --- eerrrr - poor!
Make sure you're at least 2021 feet if you pass over Fleetlands, watch out for that little triangle of Solent which drops to 2500' just NW of Fleetlands too and remember Lee has gliders!