The universal 'one bag only' rule, for security purposes, has now been abolished.
However each airline is still free to impose their own rules upon travellers, with many of the budget airlines rigorously enforcing 'one bag only'. In particular, Ryanair staff check to see that each passenger only takes one bag (within their size limits) on board the aircraft. If you've got more than one bag you'll be required to fit one inside another. (That includes laptops, handbags and post-security shop purchases). If you can't do so, you'll either be made to pay a hefty surcharge or simply be refused travel.
Other airlines might have rules which allow passengers to take more than one item on board (particularly if they're travelling 'business class' or 'first class', with a full-fare airline) or be a little more flexible with their interpretation of the 'one bag' rule.
So, since you've not told us which airline you'll be travelling with, it's impossible to provide you with a definitive answer.
Chris