See here:
https://support.apple.com/en-gb/HT201265
However websites where you work through pages in order (e.g. to search for flights, then to book them, then to add any extras such as hold luggage and finally to pay for them)
need cookies so that their servers can identify the fact that the second part of the transaction is coming from the same computer as the first (and so on).
Remember that there are alternative ways to get to Barcelona. If I recall correctly, you're in south-east England, so I assume that you're planning to fly from a London Airport. That gives you these options:
BA from Heathrow to El Prat.
BA from Gatwick to El Prat.
easyJet from Gatwick to El Prat. (Also from Luton & Southend, although they're probably a bit out of your way).
Monarch from Gatwick to El Prat.
Norwegian Air Shuttle from Gatwick to El Prat
Ryanair from Stansted to El Prat (although, again, that's probably not close enough to you).
Vuelling from Gatwick to El Prat.
Ryanair from Stansted to Reus.
Thomas Cook from Gatwick to Reus.
Thomson from Gatwick to Reus. (Also from Luton).
Ryanair from Luton or Stansted to Girona.
Thomson from Gatwick to Girona.
(Both Reus and Girona are about an hour away from central Barcelona by direct coach).