London Welsh let a 16 point interval lead slip at home against Moseley in their first round clash last weekend as they slipped to a 24-21 defeat. Swansea were beaten at home by Ulster A, 33-12, in their first outing in October.
The game will be played a week short of the 125th anniversary of the first meeting of the two clubs at St Helen's on Christmas Eve, 24 December, 1885, and will be the 99th game between the two old rivals..
"There's always been a massive rivalry between the two clubs over the years and we want to show people in Wales that London Welsh are an attractive side to watch, with ambition on the field as well as off it," said former Wales and British Lions back row star John Taylor, who is currently the managing director of London Welsh.
Welsh Clubs in British & Irish Cup action this weekend
Saturday, 18 December
Ayr v Llandovery (3pm)
Llanelli v Nottingham (3.30pm)
London Welsh v Swansea (1.00 pm)
Pontypridd v Birmingham & Solihull (2.30 pm)
Plymouth Albion v Newport (3pm)
Sunday, 19 December
Neath v Bedford Blues (2.30pm)