So asking the original question, are there any circumstances in which an ELT is required?
No, there is no legal requirement to carry an ELT on European light aircraft - but of course you can if you wish.
In spite of my earlier comment I am not opposed to ELTs. The problem with regulations is usually if someone decides the carrying of an ELT is a good idea it simply ends up in indiscriminate legislation. In other words what will actually happen is all aircraft from microlights and gliders upwards will be required to carry an ELT and it will have to be a panel fit and it will have to be re-certified every year.
There are many aircraft that rarely do more than operate around the local area. There are few remotely desolate areas in the south of England these days!
There are also pilots who are prepared to cross channel without a life raft, life jackets, ELT etc. Personally imho that is their call, in the same way as some one else commented, you can go fell walking or mountain climbing or set sail across the channel without telling anyone and without any safety equipment. Stupid - probably, and if the RNLI find you be prepared to make a hansom donation. However, we don’t need any more regulations and we especially don’t need any more indiscriminate legislation. If a pilot is not intelligent enough to realise some or all of this equipment might be warranted in some circumstances and he decides not to carry it in my view that is his look out.