If your reservation does not include checked baggage, you can either amend your reservation prior to the flight, or instead show up to the airport and check in baggage at the check-in counter. Both services will cost money, how much depends on the route and the date flown.
Using the WizzAir baggage fee calculator, with Poznan-to-London entered as the destination (plus a random date in April for travel), I see fees of €29 for adding checked-in luggage to your reservation after initial booking, and €60 for checking the bag in at the airport. There is a slightly higher fee for a larger/heavier bag. (The fees are also listed in Euro; I don't know if they'll accept PLN or pounds or require you to pay by card if you go to pay the fee at the airport on check-in.)
This is why the free checked bag policy for carry-on is such a big deal. If you pack a small enough bag and follow the restrictions set by security, etc, for carry-on luggage, they will waive the fee if it turns out they need to check it.
So, to be clear, the policy is that hand luggage is free. If they run out of room for hand luggage, they will check your bag(s), but it will remain free. If you want to explicitly check your bag, then it is no longer hand luggage (even if it meets the size constraints) and you'll need to pay the requisite fees for checked luggage.