That's going to be a bit tight, but definitely doable.
Easyjet flights depart from Terminal 2C (they arrive at 2b). Similar to LHR, that's separate buildings, and you would not want to have to walk back....
Getting through customs and immigration should not be a long wait. The BCN airport was eerily deserted the last few times I've been through it. Also, there's not many non-EU arrivals, so there should be no long queues at immigration/customs.
Priority baggage delivery is hit-and miss - don't count on it. But BCN has a very modern and quick bag delivery system. Getting one's bags 15 minutes after deplaning is common there.
In my experience, going from T1 to T2c takes around 45-50 minutes all in all. But then, I have an EU passport and never had to wait at immigration at all.
Easyjet is more than strict with their check-in cutoff time (normally 40 minutes prior to departure). 10 seconds later than the time printed on your BP and you won't be accepted for the flight anymore.
Do OLCI, so you'll have your boarding passes already. In case you're running late that'll give you an additional 20 minutes - if worst comes to worst you'd need to check your bags at the gate. EasyJet closes the gate 20 minutes prior to departure.