Shaun James forms a new centre partnership with Tom Shanklin while Nick Macleod and Dean Dewdney continue at half-back. New faces in the pack are Craig Quinnell, recovered from a calf injury, and Mark Lewis.
Joining Budgett among the replacements are Rhys Thomas and Matthew Nuthall, both of whom played for Cardiff in the Premier Division win over Llanharan last weekend.
Dan Baugh will also travel north with the squad.
Unavailable for selection due to injury and illness are Tristan Davies, Ben Evans, Ken Fourie, Ryan Powell, Jamie Robinson, Nick Robinson, Nathan Thomas, Jonny Vaughton, Nick Walne and John Yapp.
Blues team v Edinburgh Rugby: Rhys Williams; Fereti Tuilagi, Shaun James, Tom Shanklin, Craig Morgan; Nick Macleod, Dean Dewdney; Gethin Jenkins, Gareth Williams, Martin Jones, Craig Quinnell, Deiniol Jones, Mark Lewis, Kort Schubert, Martyn Williams (capt)
Replacements: Rhys Thomas, Andrew Lewis, Robert Sidoli, Nathan Budgett, Lee Thomas, Richard Smith, Matthew Nuthall
Referee: Alain Rolland (Ireland)
The match is televised on Setanta Sports - Sky subscription channel 429 and is shown live in the clubhouse at Cardiff Arms Park.