This may sound obvious, but if you want to catch bigger carp you need to fish where the bigger fish are. A lot of commercial fisheries are well stocked with smaller fish and while this means you will catch fish more often, the chances are that they will be small fish. So, the first thing you need to do is a bit of homework. Ask around about venues where bigger fish are to be found.
Having found your venue, try to locate where in the lake the big fish end to lie. One obvious way to do that is to look to see which pegs the specimen hunters always head for. As a rule though the big fish like areas where they feel relatively safe. That often means areas that are hard to cast to or where there are snags. Catching the big fish often means having to be very good at casting to the right place. Other tips include watching for signs of fish movement, locating areas where the fish might patrol (eg between islands or close to banks that are not accessible to anglers).
Next, sort out your bait options. If you can't use boilies, I personally don't rate them that highly anyway. Granted they stay on the hook very well, but I have found that really hungry carp prefer other baits (and I have had five 30+ pounders and several 20s this year, so I think I can prove it). Sweetcorn is a good bait, but you have to be prepared to let it lie on the bottom undisturbed for long periods - hours at a time. That can be a bit disconcerting because we have all had the experience of winding in and finding that there is no bait left on the hook! Other baits to try include luncheon meat, chick peas, prawns, Pepperami or drilled pellets (Dynamite Baits do really good halibut pellets that the fish love, but you will need to change them every couple of hours as they soften and can then come off the hook). Hair rig your bait for best effect. Another respondent has suggested using bigger baits. That actually is a perfectly good tactic. Small fish can't get big baits into their mouths so lumps of bait maybe 20mm across will only be able to be picked up by big fish. If, for example, you are using luncheon meat then do give big lumps a try.
Bait up your chosen swim a bit. Fire free offerings into the swim, and be as accurate as you can. Alternatively (or as well as doing that) put some free offerings right next to your bait by using pva bags.
If you have been float fishing, change over to ledgering. The bait won't move around on the bottom like it can when you are float fishing. Moving bait in still water will disturb big fish and they won't touch it. I'm assuming that you know about rod pods, bite alarms etc. You don't actually need them, but they do help a lot and my advice is to equip yourself with these accessories so that you can actually take your eyes off your rods sometimes. What you definitely will need are bait runner reels. Without them you will be in severe danger of having all your gear disappear into the lake if one of the monsters does decide to have a go!
A lot of people like to experiment with rigs (chods, stiff links, helicopter rigs, you name it) but I prefer to keep it simple. I simply use a hair rig a 14" braided leader, with a running lead.
If you are fishing a specimen lake be prepared not to catch anything at all on some visits to the water. Venues with really big fish (I'm talking 20lb plus) tend to be relatively thinly stocked. With only a few fish in the water it is obvious that you won't catch as often. Your long days of getting no bites are common amongst carp specimen hunters.
Catching big carp is all about patience, persistence and constant thought and reflection on what the fish are doing. Many are the times I have seen some small clue or had a little idea which has led me to make a small change to my tactics that has resulted in a catch. Specimen hunting is a very different kind of sport to match fishing or even an afternoon at the local commercial fishery.
Hope that gives you some food for thought. Tight lines.