Apart from the security regulations relating to cabin baggage, each airline is free to make its own rules regarding pushchairs and prams. So you should check the relevant airline's website for information (or post again, stating which airline you're travelling with).
However, the majority of airlines permit you to
check in one
fully collapsible pushchair per child, in addition to your own checked baggage allowance. For example, see Ryanair's rules here:
http://www.ryanair.com/site/EN/faqs.php?sect=b ag&quest=checkedbaggageallowance
and BA's rules here:
http://www.britishairways.com/travel/bagchk/pu blic/en_gb
Prams and pushchairs which are not fully collapsible are, to the best of my knowledge, not accepted as checked in baggage (or as cabin baggage) by any airline.
With regard to hand luggage, the security rules (which apply to departures from all EU airports) on the Department for Transport website state "Pushchairs, walking aids and wheelchairs are usually permitted but will be security screened. You should check with your airline.":
http://www.dft.gov.uk/transportforyou/airtrave l/airportsecurity/requirements
Ryanair appears to allow pushchairs to count as cabin baggage (in addition to the 'one item' rule which they apply):
http://www.ryanair.com/site/EN/faqs.php?sect=b ag&quest=cabinbaggageallowance
but BA makes no mention of them:
17:01 Thu 09th Oct 2008