Most European low cost airlines have wised up by now -- probably I am not the only one who will squarely refuse to fly if two bags are not allowed. (Both of my bags are quite small). This typically is an extra thrown in with some more expensive kind of fare -- you can't buy a second bag by itself. Wizz Air policy
PASSENGERS WITH PRIORITY BOARDING
are allowed to carry 1 additional personal item in addition to the small or large cabin bag.
easyJet Plus, FLEXI fare, Upfront and Extra Legroom customers
Plus ONE additional small under seat bag (For example a handbag or laptop)
Maximum size of 45 x 36 x 20cm which will need to be placed under the seat in front.
Even Transavia have found out which side of the bread is buttered and now say:
If you’d like to take an extra piece of hand luggage with you, we recommend the Max fare. These are the conditions:
1 piece of max. 55 x 40 x 25 cm and 1 accessory, such as a handbag or laptop bag, that fits under the seat in front of you. The weight limit is 10 kg, divided over 2 pieces of hand luggage.
(back in 2016 April they insisted on a single luggage)
In 2016 July, WOW Airways unblacklisted itself and now allows for a personal item and in a refreshing change they even display the size of it:
In addition to this, guests may board the plane with one personal item such as a laptop, a small purse or camera bag (max 42x20x20cm); and a duty free shopping bag.
In 2017 September, Ryanair changed their policy and while they still allow for two bags, the big bag now goes into the hold free of charge unless you bought Priority boarding. This is different from the airlines above where you needed to pay to carry the small bag on board, Ryanair wants you to pay to carry the large bag on board. (I personally would not be surprised if other airlines would follow suit to speed up boarding.)