Player-coach Britton only became assistant manager last month after Claude Makélélé's departure but oversaw a 1-1 draw with Crystal Palace at the weekend after Paul Clement was sacked last week.
Yet though the Englishman retains no desire, as of yet, to become a permanent boss - Swansea showed fight to earn a point, doing so for the first time this season in a game that they have also conceded.
The relegation-threatened Swans are four points from safety at the half-way point of the campaign and have won just three games all season, but at least showed improved intensity in their first game under 35-year-old Britton.
But they face a fierce test on their trip to Anfield, with Liverpool - though they have drawn more home games than they have won until now - fully capable of blowing them away with their attacking ability.
The Reds kick-started the top-flight's festive period with an engrossing 3-3 draw at Arsenal on Friday night, having surrendered a two-goal lead within just five second-half minutes to trail 3-2.
While they overcame a brief wobble to earn a point, Liverpool had the chances - and control - to win comfortably and will hope not to be left frustrated once again here.
They have drawn five times in front of their own fans this season including all of their last three home matches, scoring just two goals in three games since their last Anfield win over Southampton.
That is a marked contrast from the form of Jürgen Klopp's side away from home, Liverpool having won four matches and drawn one - scoring 19 - of their last five on the road.
They will hope to get back to winning ways on home soil, especially as Swansea have lost eight of their last 11 league games and last won away from home four months ago at the end of August.
And their form means the threat of relegation is very real for the South Wales side, who have been in the bottom three at Christmas in both of the two previous seasons but finished 12th and then 15th.
Yet this season appears like it will be the one in which they fail to recover and add to the 11 clubs - of 18 - since 2011-12 who have gone down having been in the relegation zone on December 25.
They have scored a mere 11 goals in 19 games, scoring more than one goal in a single game on just two occasions, meaning that Liverpool, if they can find their attacking verve, could put the game beyond them with a two-goal lead.
The fourth-placed hosts will be overwhelming favourites and with Manchester United, Tottenham Hotspur and Chelsea all facing winnable fixtures earlier in the day - the pressure will be on them to ease some Christmas-induced hangovers with a win.
Liverpool are without captain Jordan Henderson after he suffered a hamstring injury in the draw at Arsenal and had to be withdrawn, while centre-back Joël Matip remains out with a thigh injury.
Elsewhere, full-backs Alberto Moreno (ankle) and Nathaniel Clyne (back) remain absent with Andy Robertson and one of Joe Gomez or Trent Alexander-Arnold likely to start.
Midfielder Adam Lallana could be in line for a first start of the season as Klopp continues to rotate his squad to deal with the club's fixture congestion, meaning the likes of Alex Oxlade-Chamberlain and Georginio Wijnaldum could also start.
Daniel Sturridge could return to the match-day squad after returning to training on the eve of the Arsenal clash from illness.
Swansea have a number of injury issues to contend with, Wilfried Bony (hamstring), Leroy Fer (back) and Ki Sung-Yueng (calf) all absent from the draw against Palace.
Bony and Ki remain unavailable while Fer is still a doubt, but Kyle Naughton is out of contention after picking up a groin injury last time out. Midfielder Roque Mesa also had to be taken off against the Eagles after taking a knock to the knee.
Àngel Rangel is likely to replace Naughton while underwhelming on-loan midfielder Renato Sanches could come back into the starting line-up if both Fer and Mesa are ruled out.
Recent form (all competitions)
Swansea City: LWLLD
Arsenal 3-3 Liverpool
Swansea City 1-1 Crystal Palace
Swansea have won two of their last three meetings with Liverpool after failing to win any of the previous eight (D2, L6).
The Welsh club's victory at Anfield last season was their only triumph on L4 in 16 visits in the league (D3, L12).
The past nine league meetings between these two clubs have produced 35 goals - Liverpool scoring 22 and Swansea netting 13.
Liverpool have not lost a league game at home on Boxing Day since a 1-0 defeat to Manchester United in 1986, winning seven and drawing three since then.
Swansea have not won away on 26 December since a League One win at Crewe Alexandra back in 2006, drawing two and losing two of four attempts since then.
Liverpool forward Roberto Firmino has three goals in three Premier League appearances against Swansea.
The only two Liverpool player to have scored as many Premier League goals as Mohamed Salah (15) before Christmas Day are Robbie Fowler (15 and 16) and Luis Suárez (19).
Kevin Friend is the man-in-the-middle with this his 10th Premier League game of the season, having overseen Liverpool's home wins over Crystal Palace and Huddersfield Town.
The 46-year-old - who was the referee for Swansea's 2013 League Cup triumph - has not officiated a game involving the Swans since April, a 1-0 defeat at West Ham United.
He has dished out 23 yellow cards and no red cards in the top-flight so far this term.