The FDA General Secretary told BBC Radio 4's Today programme that the success of exit from the EU was threatened if Whitehall was not adequately resourced.
Penman said: "If you take those resources from elsewhere within government spending, it threatens the delivery of public services.
"That's the reality, you can't have your cake and eat it.
Penman went on to stress that without more resources, "Brexit will simply mean a further cut in public spending - because departments will have to cut other work to deliver the resources that are required to support the new policy areas or support the negotiating process itself."
Listen to Dave Penman speaking on air here. This topic is covered from 54 minutes and 8 seconds into the recording.
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Senior civil servants warn over Brexit resources funding