With respect to the question of what is UK Territorial Airspace.
It is the airspace that overlies the United Kingdom of Great Britain and Northern Ireland and the surrounding islands plus the territorial waters which extend to 3nm off shore
It does not include the Channel Islands and it does not include the Isle of Man.
However, The State of Jersey, the States of Guernsey and the Isle of Man have all provided for the IMC rating in their legislation within their own territorial airspace - again, the land mass plus their own territorial waters.
If you want to see how far UK territorial airspace extends from the coast you need to look up the extent ot the UK's territorial waters.
The validity of the IMC rating for flight in IMC does not extend to the airspace over the high seas.
So IMC rating holders are limkited by national territorial limits and not by what may be the FIR boundary.
For example since it was previouslt mentioned, Parts of Northern Ireland (UK territorial airspace) lie within ther Shannon FIR since the FIR boundary does not follow the land border. Therefore it is entirely legal for an IMC rating holder to fly in IMC within those parts of the Shannon FIR (Class G) that overlie Northern Ireland. But it is not legal for then to fly in IMC in the Scottish FIR where that is within the territorial airspace of Ireland (Eire).
On the same thred, it is not legal for an IMC rating holder to be flying in IMC half way between England and Guernsey since this is over the high seas and outside both the UK and States of Guernsey Territorial airspace.
So getting back to the "How far across the channel can I fly in IMC with an IMC rating?" the answer has to be 3nm from the UK coast i.e. the limit of the UK.
Simple?