This is an old chestnut of the way UK airspace is managed
In practical terms, you have two watertight airspace compartments:
1) the "commercial" airspace, which is mostly Class A and is handled by London
Control, Manchester Control, etc, and is 100% radar control airspace. These controllers provide zero service to VFR traffic, and they don't handle flights below a certain level, or more specifically outside controlled airspace. In this airspace, you get the seamless IFR enroute clearance/service which European IFR pilots are used to.
2) the "stuff below" which gets a FIS from London Information, etc, and the occassional radar service from units like Farnborough.
The two compartments don't really connect up - unlike say France where there is a lot more integration.
The bottom line is that if you enter UK airspace, on a Eurocontrol IFR flight, and you find yourself outside controlled airspace (even briefly), you will not get a handover to London Control. You will get handed to London Information, which amounts to an eviction from ontrolled airspace and if you want to get back in, you have to get LI to negotiate a new IFR clearance for you
This is a common issue from France to the UK which catches out a lot of pilots.
There are two ways to solve it.
One is to leave French airspace at a level which is fully in CAS and more to the point at which you are being serviced by Paris
Control. From conversations with non-UK ATCOs it appears that Paris Control have a letter of agreement with London Control for a direct handover. In practice, I have found, this means you want to leave French airspace at FL120 or higher. Quite often, on a nice day, one is crusing across France at say FL100 (no oxygen needed, etc) but if you are heading for say somewhere halfway up the UK, and want the weather avoidance options which you get in IFR, you want to climb to FL120 before Paris Control hands you over.
The other is to pick a route which is 100% in CAS; this is quite restrictive because there are not many such airways.
From Jersey to Ireland, I don't know the best solution but one way would be to file a route initially up via ORTAC, which remains in CAS and then once over the UK, turn west and head to Ireland. Looking at an old VFR chart I have on the wall, N862/N864 to BCN and then to STU, FL110 rising to FL150, etc to remain in CAS. If, out of Jersey you file a more direct route over say Plymouth, or if you fly N862/864 at say FL090, this will be Class G (below FL200, I think) and you will get dumped onto London Information...
I don't see a way to get from Jersey to Ireland, with a continuous IFR clearance, unless you fly the airway routes and are capable of FL150 around STU.