Can anyone tell me what the benefits regularly eating oily fish? The UK Food Standards Agency talks about "Eating just one portion of oily fish a week has clear-cut health benefits. " without saying what specifically it is about it that helps, and in what way.

Oily fish are those rich in OMEGA-3 oils, DHA and EPA, which are the active beneficial components of the fish oil. These two heavy oils are associated with cardiac benefits and a lessenened tendency to form plaque in cardiac arteries, although the mechanisms by which they accomplish the benefits aren't completely clear.
One of the many benefits seems to be through "blood thinning."

And, of course, eating TWO or more portions of oily fish is even better.

<If I weren't going to the dentist this afternoon :(, my lunch would be sardines! :D>

And, of course, eating TWO or more portions of oily fish is even better.

You mean per week?

Also I hear of concerns regarding mercury content, particularly if you eat fish regularly (and therfore increase intake of pollutants).

Yes,
Per week...and probably eating even THREE meals of fish per week is better yet.
And there's nothing easier than opening a can of sardines or tuna for lunch.

Mercury scare is probably overrated. After all they are still letting dentists put amalgams made of 50% mercury in our mouths...to be slowly absorbed til the day we die.

Mercury is one of the most dangerous substances known to man, probably second overall.

Certain types of fish are known to carry more Mercury risks than others.

And some countries have banned the use of amalgams(silver fillings) for dental use. More and more dentists in the US have stopped using amalgams, also.