Tesco have a cross cut (not strip cut) shredder for just £9.97
It's manual operation rather than electrically powered as most cross cut ones are, but is ideal for home use.
Multi Media Cross Cut Shredder CD04
Ideal for sensitive data on paper, credit cards and CDs. Shreds credit cards into 3 pieces, CDs into 126mm strips and paper in 3 x 22mm strips. Manual operation.
Cutting type: paper crosscut
Plastic Waste Bin 4 Litres
Feeding opening: paper 216mm
Cd: 126mm credit card: 58mm
Dimensions: 280 x 240 x 150 mm
Bar Code: 5012236017603
It's available online through the groceries section (sign in required), or pick one up in your local store.