Haven't flown round there for a long while, but it used to be easier to talk to Bournemouth who control a lot of the stuff up to 3000' - the map used to say see note x and all the info was in the legend.
Once talking to Bournemouth, they could negotiate any further clearance and then hand you on to solent.
Unlikely you'll get clearance above 2000' through solent though, as they'll be vectoring stuff all the time and you'll be going right through their approach. More chance if you go through the airfield overhead.
And forget your MSA stuff, if you're flying visually it has no use at all. 15-1700' is ample around there.