Joseph will join Guy Armitage in the centre, with Kieran Low joining Bryn Evans in the second-row and Mike Mayhew again starting at hooker.
Cardiff Blues director of rugby, Phil Davies, has named a line-up depleted due to international call-ups.
The Blues have no chance of making the LV= Cup knockout stages and are without Wales trio Sam Warburton, Jamie Roberts and Leigh Halfpenny.
Jason Tovey, Rhys Patchell and Michael Paterson all start for the home side.
Cardiff Blues: 15 Jason Tovey, 14 Owen Williams, 13 Gavin Evans (capt), 12 Dafydd Hewitt, 11 Harry Robinson, 10 Rhys Patchell, 9 Alex Walker, 8 Robin Copeland, 7 Thomas Young, 6 Michael Paterson, 5 James Down, 4 Cory Hill, 3 Benoit Bourrust, 2 Rhys Williams, 1 Nathan Trevett.
Replacements: 16 Kristian Dacey, 17 Sam Hobbs, 18 Taufa'ao Filise, 19 Luke Hamilton, 20 Rory Watts-Jones, 21 Lewis Jones, 22 Ceri Sweeney, 23 Chris Czekaj.
London Irish: 15 Tom Homer, 14 Topsy Ojo, 13 Jonathan Joseph, 12 Guy Armitage, 11 Marland Yarde, 10 Shane Geraghty (c), 9 Pat Phibbs, 8 Chris Hala'ufia, 7 Jebb Sinclair, 6 Matt Garvey, 5 Bryn Evans, 4 Kieran Low, 3 Halani Aulika, 2 Mike Mayhew, 1 Max Lahiff.
Replacements: 16 Davey McGregor, 17 Jerry Yanuyanutawa, 18 Leo Halavatau, 19 James Sandford, 20 Alex Gray, 21 Steven Shingler, 22 Ian Humphreys, 23 Jack Moates.
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