Aaarrghh Nitrates Through The Roof

Long story but will try to be quick. My main filter pump packed up 4 months ago so I put an old one back in that isn't quite good enough for the size of tank. 3 weeks ago my husband mended the proper one so I put it back in but have kept the old one running as well as an extra precaution.
A week ago I bought a new tank that I am setting up as a reef tank. unfortunately it came with a dozen tropical fish too. I put the angel fish in a new tank of their own and added the 8 mollies to my aforementioned tank. The other fish though that i acquired is a very large plec almost a foot long.
My tank is 119 litres and apart from the new fish I already had 6 harlequins, 6 cardinal tetras 2 mollies, 2 small plecs and 2 yoyo loaches. The additional 6 mollies probably took it up to capacity but the big problem is this huge plec - it's 11 inches long. Eventually it will go in my current reef tank (which will be cleaned an converted)when the new one is up and running but this may not be for several months.

The new Plec is so big its been uprooting plants and stirring up the substrate, so today I decide to remove the now floating and broken vegetation, and clean out the filter pumps. the old pump is the sort with just a foam pad in it that you clean.....well, the smell that came from that was unbelievable. It was only around 4 weeks since last cleaning it, (although I had changed cleaned the good one and replaced some of the media in that a fortnight ago) it smelt like very overcooked sprouts.

This prompted me to test the levels and I have found the nitrates to be on 80 !! (ppm mg/l)
nitrites appear to be zero

I'm guessing this is due to a combination of the sudden extra fish and the plec stirring up the substrate. I do clean the substrate every water change each fortnight but the tank is 4 years old and it's impossible to clean it all.

Anything you can recommend to get the nitrates down?

I agree, water changes are the best way to get nitrates down quickly. Long term, lots of well growing plants will help too.
But as fcmf suggests, small daily water changes are the best way to start as other things will have built up too (things we can't measure) and changing too much as one go at the start will change the water too much. After a few small water changes, you can increase the amount. What is the nitrate level in your tapwater? This is the lowest you can get the tank nitrate by water changes alone.

The problem is most likely to be the plec. They are well known as big waste producers and as such will feed a lot of ammonia into the start of the nitrogen cycle. Are you sure you want to keep it? If not, rehoming it as soon as possible may be the best for your tank.