But, despite this, the 36-year-old wouldn’t change a thing about his life.
Speaking exclusively to Closer Online about juggling parenthood with a busy career, Jeff stressed that the key is to be organised.
He said: “Bobby’s 12 and Freddie’s very nearly 11 and obviously the summer holidays are as much of a problem to me as they are any other busy working parent who relies upon the time they have, you know, in office hours, to kind of make everything work.
“When the kids are around as well, very often something’s got to give, and often you’re still trying to work and the kids aren’t really occupied, they’re going to distract you, it causes arguments, you know I think you have you have a very clear plan.
“Or, at the very least, have a little bit of a menu to get through in the easiest way possible.”
Being the sons of Jeff and the late Jade Goody, Bobby and Freddy have grown up in the spotlight. But Jeff has withdrawn them significantly to give them the chance of a normal childhood.
“Fame doesn’t faze them,” Jeff insisted. “If anything, the criticism that I’ve received since is that I’ve made them un-famous. I don’t think they’re really serious about it, but that has been thrown my way at times.
“That was a conscious decision that I made six years ago... that they needed a normal childhood to come to terms with their loss.”
Jeff has been dating Kate Dwyer since last year and, thankfully, her introduction to his boys went relatively smoothly.
He said: “For me, six months [in a relationship] is a really good amount of time, because you know by then whether or not they’re likely to be around for the foreseeable future.
“The weekend [that I introduced the boys to Kate] we went to the London Aquarium, we went to the London Dungeons, we did a couple of really cool things.
“It felt like the perfect introduction because the boys seemed suitably impressed by her, and she got to answer all of those doubts that would go through someone’s head who’s meeting somebody’s children for the first time.
“Everyone was happy with it and how it went.”
And what does Jeff like to do if he does get some time away from work and daddy duties?
“I love going on walks, clearing my head, deciding, planning and talking to my partner,” he said.
“She’s wonderful and I always want to run everything past her because I trust everything that she says. Just little day trips, I like little picnics.
“Simple stuff, I’m easily pleased. I don’t need to go anywhere sensational – I feel like I get to do all of that with work. What I want is to be able to slow down and just be in the moment and not worry about what needs doing, because that’s what life as an adult and a parent generally consists of.”
Jeff has teamed up with the Family & Friends Railcard, to offer 21 top tips for surviving the summer holidays with kids – something he knows all too well can be tricky.
He added: “If you’ve got your week planned out, then everything goes as smooth as possible, and everyone gets to do what they want to do.
“Whereas if you do it off the cuff and you’re scrambling round to get things sorted out last minute, then generally things go wrong, people get upset, arguments happen, then the harmony within the house just goes up in smoke.”
Check out the Family and Friends Railcard's top 21 tips on surviving the summer holidays here!