Will 180mm rotors fit my Carrera Vengeance Ltd. Edition bike?

Start by measuring the diameter of your current disc. If it is 180, the change will be very easy.

If you have 160, I'd keep trying (to find that size). In a quick search I did just now searching "Clarks M3 hydraulic disc brake set" the first result I got was a 160mm set. There was a run on bike parts for a while, but I think that is slowly winding down. If you need and want the 160 set, I bet you'll find it.

May I ask why you want that set in particular? Nothing wrong with it, and there is nothing wrong with liking a product just because you like it. I have my preferences for sure. Its just that there are so many choices out there.

The question may come up, if you have 160 now, is it OK to move up to 180. You could, with different adapters for the calipers. However, this will create more braking forces that translate into the fork and frame. It would probably be fine, but I'd check with someone at Carrera or your LBS to be sure that those extra forces won't damage the frame. I am not familiar enough with Carrera to say confidently.

As long as the kit includes the correct caliper mount adaptors, it will be fine. You can buy them separately if you need to. It looks like bike has post mount fork and IS on the frame so it's likely you will need to buy at least one of those in addition to the kit.

the 'Limited Edition' seems to date back at least a decade in various specs, so the question is hard to answer

looking at the one on the current Halfords website it has an SR Suntour XCM30 fork of some unknown MY and mechanical disc brakes

https://www.halfords.com/bikes/mountain-bikes/carrera-vengeance-limited-edition-mens-mountain-bike---xs-s-m-l-xl-frames-216878.html

this 10 year old version

http://web.archive.org/web/20110414134431/http://www.halfords.com/webapp/wcs/stores/servlet/ProductMobileDisplay?catalogId=10151&storeId=10001&productId=786835&categoryId=165499&langId=-1

had

RockShox Dart 1 forks with 100mm travel and pre-load adjustment Shimano 24 speed gearing with Alivio rear mech, great for hill climbing New Shimano BR-M445 hydraulic disc brakes provide strong and powerful braking performance

Generally speaking disc brakes used to mount with something called 'International Standard' and since about 2007 this switched almost exclusively to 'Post Mount'. In earlier years before IS there were proprietary manufacturer-specific fittings as well. In recent years we now have 'flat mount', which is supposed to look better on road bikes and now appears on MTBs as well.

Chances are you have Post Mount, but you'd need to look at the fork AND the rear disc brake to see that.

According to Clarks, it is PM & IS compatible

http://www.clarkscyclesystems.com/product-range/brake-systems/hydraulic-disc-brakes/m3-hydraulic-brake.html?att_color=40&attr_diameter=229&attr_wheel_option=224

It looks like the brake is natively PM, and has an IS adapter supplied.

One issue is that you are buying a set https://www.chainreactioncycles.com/clarks-m3-hydraulic-disc-brake-set/rp-prod162155

This comprises rotors and brakes. However it's very possible that your rotors attach to your bike using 'centerlock'. These ones are 'six bolt'.

Compare centerlock

If you have centerlock now, then six bolt won't be a good purchase, because it will need an expensive adapter to fit your bike, and it's just generally a bad idea

In addition, you can check rotor wear with a caliper, but unless they are worn, these are fairly basic discs that likely won't be an upgrade on what you have fitted already

If they are rusty or worn out AND you have six-bolt rotors already, then that's not a problem.

As far as 180mm vs 160mm goes, the size of your current rotors will be marked on them. Whatever you have now is fine. If it's bigger then you'd need to check the specs for the fork. A fork might not be rated for 180mm. In addition, the fork will have a native brake size, typically 160mm, so if you fit a 180mm rotor, then you will need to fit the brake with an adapter for 160mm to 180mm. Here's the Clarks model

You would need to check if you have the adapter with the 180mm set, or if you have 180mm brakes fitted already then re-use it. Either way the adapter is no big deal, but it's something to consider.

Otherwise when buying hydraulic brakes you'd typically focus on lever design. For MTBing a lot of people like short levers for 1-finger braking, which adds control. For touring longer levers are common. I am not quite sure what lever design is on the M3, but it looks unusual, so you might like to review that aspect.

Also, if you remove the brake calipers from the bike (without disconnecting the hose), which should just require an Allen key, then you can review the model number, etc. to find the current specs and what adapter, if any is fitted. This will help with your purchase. And check the rotors at the same time - marked diameter and centerlock vs six bolt.