Removing the cast (Cameron Harris, Brendan and Emily Murphy, Chris Lehec and Jenny Bede) we are left with:
Week 1
Clinton's Dress Tom Johnstone
That Gordon Brown Terry Newman
1D Glasses Tom Johnstone
Dedward Adam Morley (but written with the cast)
Under Labour Martin Malcolm
To Be Posh, Tory Terry Newman
Jackatony Tom Johnstone
Kirsty Wark meets Dave Tom Johnstone
I'm Past My Prime Louise Thomas
Hague and Ffion Tom Johnstone
Prince Charles and Neddy David Salisbury
Work Til 95 Martin Malcolm
BoJo's Bikes Lee Stephenson
Diamonds Are A Girls Best Noel Christopher
Chav Miliband 2 Jenny Harris (but with help from Emily Harris)
Hague Stig gag ?
Pope and victims gag Martin Malcolm
Clearasil spot fixing gag ?
Rooney score grand gag ?
Jordan on Divorce David Salisbury
Sunbed gag Martin Malcolm
week 2...
Clinton's Dress Tom Johnstone
That Gordon Brown Terry Newman
1D Glasses Tom Johnstone
Dedward Adam Morley (but with cast)
Under Labour Martin Malcolm
To Be Posh, Tory Terry Newman
Jackatony Tom Johnstone
Kirsty Wark meets Dave Tom Johnstone
Hague and Ffion Tom Johnstone
Prince Charles and Neddy David Salisbury
Work Til 95 Martin Malcolm
BoJo's Bikes Lee Stephenson
Diamonds Are A Girls Best Noel Christopher
Chav Miliband 2 Jenny Harris (but with help from Emily Harris)
Hague Stig gag Nick Hallam
Pope and victims gag Martin Malcolm
Clearasil spot fixing gag
David Haye gag Jenny Harris (but with help from cast)
George Michael gag Martin Malcolm
TUC Strictly gag Martin Malcolm
Natascha Kampusch Martin Malcolm
The ? indicate a writer isn't stated. So it does seem a number of sketches do come from outside, however they don't seem to be dropped from later shows like other sketches, whether that's accident or design.