(In the UK at least) there is no VFR at night, inside or outside CAS.
To transit the Solent Class D at night you'd need a SVFR or IFR clearance.
Note that SVFR is only available in Control Zones i.e. the CAS must start at ground level, which can be a limiting factor in what levels are available.
Also, SVFR must be given standard separation from other SVFR and/or IFR. This would probably be 3nm laterally and/or 1,000ft vertically in the Solent area.
MATS Pt 1 states SVFR flights must not hinder IFR flights so the separation requirement is the main issue, it may be difficult to get you where you want to go and be able to do so without hindering the IFR traffic.
Assuming you can accept it*, asking for IFR might be the better option at night.
* be prepared for vectoring so I'd suggest you only ask for IFR if you have an IMCR or IR (and with the IMCR only if you're sure there are no other possible airspace issues like being potentially vectored into Class A).