Just managed to close down mumsnet by some fortuitous combination of keys... so I'll try again, this time with both hands.
Can't say about easyjet from personal experience (not since ds anyway) but Ryanair let you take a buggy (or in our case a Janè slalom+matrix so size doesn't matter) to the plane steps and it does not count towards your luggage allowance. You do pay for it in a way though as newborns cost £20 a flight... Can't imagine easyjet will be any worse than the dreaded Ryanair but they should have an faq section on their website which covers this.
One thing to watch out for (maybe not relevant to you depending on age of your dc) is that they take the buggy off you at the plane steps but in some airports they give it back to you on the luggage belt so you have to cart your child through customs along with your handluggage. Also if it's raining you may well have a wet buggy and in any case a few scratches are likely so some kind of travel bag might be useful.
"easyJet allows you to take your pushchairs, buggies, travel cots right up to the aircraft steps and/or door, where they will be taken by cabin crew and stored in the hold. We do not deliver buggies at aircraft side on arrival. They will normally be delivered with baggage on the baggage carousel. It is free to bring your childs push chair.
You can however check it in with your baggage at check-in, if you wish to do so. Full size, non-collapsible prams cannot be accepted for travel."