There's always a way to beat something. It's just about finding out how. If my units aren't as good you just have be better tactically.
I also feel like people are way more likely to help me get better when I don't cry and whine about balance. Realistically my gameplay has enough holes in it that balance is probably not the biggest factor in my losses.
Do you find the centaur comes out to late? I find my issue is that p4's or panthers hit the field so soon after my centaur that it almost always gets dived and destroyed without returning on it's investment.
I find it's a great unit, you just have to be really careful about supporting it with 6pdrs or PIAT sappers. That or have an AEC around to treadshot for maximum bait potential lol. Killed quite a few tanks by baiting with a centaur and using the AEC's treadshot to immobilize their tank when it dives. I find the centaur to usually be a better choice than the cromwell as long as you have the AT power to back it up in most cases.
Also, it's a bit micro intensive but you could give commandos a try if you're having trouble with your original problem still. They're absolutely great at breaking down support weapon play aggressively, and light gammons are basically a guaranteed wipe against raks or mgs when you throw them out of camo. They've also got smoke and demos for okw bases (it takes 2 smokes to plant a demo though). If he's smart he'll build an IRHT and completely shut down your commandos though lol, so just be aware.
I like getting vickers as my first built unit just because it really forces them to play around it even if it has kinda bad suppression, and it does a lot of damage regardless of whether it suppresses or not. You just have to be extra careful with it, especially around sturms, since it doesn't suppress that well. It allows you to establish strong area control in the first engagements of the game though, and the more tommies you get the easier it is to keep that control once you have enough rifle power to protect your flanks better.
I like to go vickers section section (so 3 sections total) into platoon CP and then get an engie, AEC, and then a commando, and if I ever lose sections I'll replace them with commandos because I find them to be more cost efficient anyway, and I usually just skip the squad size upgrade even though it's really good in order to get a tank out that much faster, and commandos compensate for the lost power there. I will get brens or sometimes mills bombs if I have the muni though. If I go sniper I'll build it as my first platoon CP unit just to get it working as soon as possible. I find if you play either of those builds well enough and get an early medic section, you can go through the early game with really minimal losses (I'm talking like single digit model losses best case scenario lol).