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I have Medion MD 84299 wireless (not Bluetooth) headphones and they work totally fine.

The problem is that once I turn on the headphone’s base station, Wi-Fi signal on my laptop becomes poor and download speed goes from 70 mbps to 2 mbps.

Is there a way to fix this?

The wireless headphones are working in the same frequency as Wi-Fi, 2.4Ghz, according to the official Medion MD 84299 user manual (PDF).

If your WiFi supports 5GHz use it. That is almost always the best solution. If not, try a different channel for WiFi -> 1, 6 and 11 are preferable.

Also try to keep the headphones' base station as far as possible from the WiFi antennae.

GabrielaGarcia has a very good answer already, but I'll expand a bit on it.

If you still got the receipt on those headphones, I'd consider returning them. They come from an era where not everybody was using Wi-Fi at home and everything using a radio went to 2.4 GHz because it's an ISM band. Which was a world of fun with older microwave ovens... Anyway, Wi-Fi was a simple enough protocol so a lot of electronics that needed a bit of bandwith ended up using some version of it. Not necessarily exactly to spec, but it didn't have to as long as it stayed within the 2.4 GHz ISM and could communicate well enough with whatever it had to (your base station to your headphones and vice versa). Which wasn't a big deal until everybody started using Wi-Fi, especially at higher speeds.

While Bluetooth and plenty of other technologies are also on that band, they use different methods to communicate. For example, Bluetooth uses a method of adaptive frequency hopping that's so fast (and the sub-bands it uses so narrow) that it's a lot harder to disrupt. It's also slower, yes, but still plenty fast for high-quality audio over headphones. And it doesn't disrupt your Wi-Fi as much, since it's less likely to be using exactly the same frequency as your router. The manual doesn't seem to indicate which exact Wi-Fi band it uses, so it might be hopping all over the place trying to find the best slot just as your router is doing the same. Who knows.

There's a chance that your wireless headphones use a lot more RF power than they really need.

Try covering some of the base station with aluminium foil - that'll block part of the signal it emits. Chances are that the headphones will still have a decent range, while the WiFi signal won't suffer as much.

I would first start with looking at your frequency use. If you have a android phone there are many free WiFi viewing apps (I run 4 different ones because each looks at different things). Get near your headphone base and see the frequency band it is running on. I would expect that it defaults to 1, 6, or 11. I would then guess that your WiFi is on the same channel right now.

Once you have this knowledge you can enact the advice already given by GabrielaGarcia. Change to a 5 GHz channel (or get a new router with both 2.4GHz and 5 GHz channels), or if you must stay at 2.4 GHz set you router to the channel furthest away from the channel your headphone base. Also separation of the two radio sources is beneficial, but will not help when you are much closer to the headphone base station.

Last, you may have your router running on a lower power setting. If so you can set it to broadcast at it highest setting (usually 100 mW at 2.4 GHz). This may also be a setting on your laptop, but turning it up will drain the battery faster.

I would recommend use of the 5 GHz band if possible as it will give you the best possible speed but it does require your laptop to have a 5 GHz receiver and older laptops do not.