Hi Giggl,
Assuming you mean football yeah?
In England we refer to them as Stadium, e.g. the Allianz Stadium.
Arena's in England tend to refer to smaller venues e.g. pop concerts.
To give you a real life example (you can google), there is a Wembley arena (smaller, used for exhibitions & pop concerts) and also next door there is the larger Wembley stadium where they play football and (only) the largest of world tour type concerts.
In terms of the retail side, we call them club shops or club stores. The items for sale tend to be referred to as merchandising products, but the location itself is the shop. "fan shop" is ok too, but club shop/store more commonly used.
Hope this helps, any further questions, just shout, lots of Brits on here 
Best regards,
Bart