EasyJet says this:
Save where the limits set locally are more restrictive, passengers are permitted one standard piece of hand baggage to a volume limit of 55x40x20cm (including wheels and pockets) (“Standard Hand Baggage”). It must fit without force into the gauges provided at check-in or departure gates. No weight restriction applies within reasonable limits — i.e. a passenger must be able to place the piece of luggage safely in the overhead storage bins without assistance.
In addition to the “Standard Hand Baggage” you may also carry:
(a) one of the following: An overcoat; an umbrella, or a shawl; and
(b) one standard size carrier bag of goods purchased from the departure airport.
Other than for the fact that Ryanair does not specifically allow (a) or (b), I think the rules are otherwise the same for Ryanair and EasyJet. Ryanair does not mention coats, shawls, or umbrellas on their page, but you could easily just wear these items or stick the umbrella in your hand luggage.