Going into last weekend’s final pool games, Llandovery had an outside chance of joining Llanelli but the Welsh outfit were unable to come away with the required bonus point when they were beaten by Nottingham 31-15 at Meadow Lane.
Llanelli have been drawn to play top seeds Bedford Blues in the quarter-final on Saturday 6 April.
Bedford finished 19 points clear of their nearest rivals Stirling at the top of Pool 2 after going through the pool stages without dropping a single point.
Bottom seeds Llanelli got through at the expense of Moseley on points difference. Llanelli managed to hold Bedford to a 25-all draw on their last visit to Goldington Road in the B&I Cup on December 17, 2011.
Bedford, who lost out to Bristol in the 2011 B&I Cup final, are searching for their first silverware since lifting the Powergen Shield at Twickenham in 2005.
Quarter Final Draw, April 5-7
Bedford Blues v Llanelli – Saturday 6 April, KO 3pm
Newcaslte Falcons v Nottingham Rugby – Friday 5 April, KO 8pm
Cornish Pirates v Munster – Sunday April 7, KO 3pm
Bristol Rugby v Leinster ‘A’– Sunday April 7, KO 3pm