Angus,

..... BTW are dogfish a nuisance...

I'll try an analogy, to some daisies are pretty flowers, to others
they are weeds.

I thought that they might offer a good bit of sport on the right tackle

they can, but like mackerel, if they are around it's pretty difficult
to catch much else, unlike mackerel, they are considered to be *weeds*

and I was hoping that I might stand a chance of a shore caught Tope.
Perhaps I'm being a little over-optimistic

I'm afraid so, it used to be possible at one time, but now 'fraid not,
but that should not stop you trying - you never know

However, all I own are present are some carp rods, so I'll have to get
something to handle larger baits, weights and rough conditions.

True, and asking "which rod" is also a holy grail type question, my
suggestion FWIW, avoid spending a shed load of money initially, just
see a local tackle dealer and get a competent setup to gain experience.

Also sea fishing is not just about chucking heavy leads around, there
are many areas, particularly in Scotland, where spinning, floatfishing
or freelining for mackerel, saithe and sea-trout etc is really good fun.
Your carp rods would be fine for some of that and also for chasing
flatties.