As John suggests, practices vary from one airport to another.
In part, that's due to the fact that staff wearing the uniforms of Iberia and easyJet at airports probably aren't actually employed by those airlines. For example, easyJet's check-in staff at Gatwick are actually employees of DHL, whereas in Spain they use Menzies Aviation for their ground handling operations. Iberia uses its own subsidiary in Spain but will use a different company (possibly such as Swissport) in the UK. Each company will have its own way of interpreting the rules of the airlines that it serves and, of course, (irrespective of any official rules) some local managers will be laxer (or stricter) than others are.
Iberia allows passengers to place one cabin bag in the overhead lockers, with that bag having maximum dimensions of 56 x 40 x 25cm and a maximum weight of 10kg when using Economy class. You can also place one personal item under your seat, which can have dimensions no greater than 40 x 30 x 15cm.
https://www.iberia.com/gb/luggage/hand-luggage/
As Fitzer states, easyJet's limit is 45 x 36 x 20cm in order that the bag will fit under the seat in front of you. The overhead lockers are reserved for the baggage of customers who've paid an additional fee. They they can add a second bag, with dimensions no more than 56 x 45 x 25 cm, to their allowance. Originally that option was only available to customers booking 'up front' or 'extra legroom' seats but it's now been extended to all passengers. (There are no weight limits for cabin bags on easyJet, as long as you can handle the bag unassisted).
http://www.easyjet.com/en/help/baggage/cabin-bag-and-hold-luggage