It's not even practice for most people.
I've mainly noticed that the level you start out at, will pretty much be the level you'll stay at for that game. (Does not apply to all people).
For me, I bought CoD4 late, and as soon as I got on, I was playing with people who's levels were a ton higher than me. I still beat them with one of the first weapons you unlock. I of course got a little bit better by using better guns, but not by much. It's just that I'm good with video game's. (I average, on COD4, about 30 kills, and about 10-15 deaths).
When I bought Call of Duty World at War, I was immediately good at it, because that's just how I am.
Try to find a way to get a keyboard/mouse working on the 360.
I know that I suck with a keyboard/mouse, but give me a 360 controller, and pretty much in any FPS game, I'll be good.
I'm have experienced exactly the same mate. The level you start at has a LOT to do with how you will fair, as you'll be playing against people with better weapons, attachments and perks, plus know the maps and strategies better. Only practice and putting in the time will fix this issue.
Regarding controllers... I've played games on my macs and pc's s since a young kid (I'm 28 now), and as soon as using a keyboard and mouse to aim/shoot and do misc stuff came into effect as 'the thing', I lost the plot entirely. It never feel natural to me and still doesn't. At that point a computer became a work tool, and I bought a PS1 when they first came out. I've been a console player ever since n don't regret it for a minute. The controllers are surprisingly comfortable, efficient and easy to use once you get the hang of it. If you think it's slower, you can tweak the sensitivities in any game. I can understand that switching must be hard, but hang in there ok!
I totally disagree that a keyboard and mouse has a huge advantage over a controller, it's all up to the operator. I can hold my own very well in Cod5&6, and have come across some absolute freaks who would put many to shame. All about practice, levelling up and learning the maps.