Brok was speaking against a background of decisions taken yesterday (28 September) by the Parliament's budgets and budgetary control committees to beef up budgeting rules for the EEAS to ensure transparency and financial accountability.
Before the EEAS can be launched, legislative changes are needed for the service to function in terms of staff rules too.
Brok made plain that the European Parliament would insist on the need for "quality and fair distribution between the institutions," stressing that according to inter-institutional agreements that had already reached, 60% of the EEAS staff should be "Community personnel," meaning officials from the Commission and the Council secretariat.
As High Representative Catherine Ashton has to fill 80 middle-management positions - as well as a senior managerial team of some ten people - before the EEAS can be launched, Brok indicated that the Parliament would only decide on the staff and financial regulations once it had approved the personnel mix and the quality of key appointments.
The EEAS is generally expected to be launched in December, marking the first anniversary of the entry into force of the Lisbon Treaty. However, Brok made clear that if the Parliament is not satisfied with Ashton's selection, this deadline could be missed.
"If we are not convinced, Parliament can delay its decisions," he said.
Brok also stressed that the Parliament was united across party lines in its position regarding the EEAS.
"On European development and integration processes, the Parliament works mostly with a broad majority," he said.
Asked about progress in Turkey's accession talks, Brok said that Turkey and also Ukraine should seek to obtain a status with the EU similar to that which Norway has at present, fully linked to the internal market and the Schengen border-free area.
As for the Roma controversy surrounding mass expulsions of Roma from France in recent months, Brok regretted the fact that the issue had been politicised in the European Parliament. Recently, two competing resolutions on the Roma issue ended up in a defeat for the centre-right European People's Party and condemnation of France.
"I think this is not a territory where political groups should play party politics," Brok said.