Currently based at Knowle Village, the club are hoping a forthcoming move to AFC Stoneham’s ground will be the catalyst for going on to win the HPL this season and progress up the pyramid.
A quick glance at the Wessex Premier shows AFC Stoneham in second place, Hamble Club in fourth and Baffins Milton, with games in hand on most of the teams above them, five points adrift of Stoneham in 10th place.
All three of those clubs were playing in the HPL until recently.
Here, The News looks at their rapid progress which Infinity will hope to use as a template if they go on to clinch promotion this term.
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Though they finished fourth in the HPL in 2014/15, the Purples still won promotion to the Wessex as none of the teams above them - champions Hamble Club, runners-up Baffins or third-placed Otterbourne - could move up a league.
Stoneham finished eighth in their first two seasons in Wessex 1 and fifth in 2017/18 before winning the title last season.
They have made a stunning start to their first ever season in the Wessex Premier, and last weekend’s 2-0 home win over Fleet moved them up to second place.
Having won the Portsmouth Saturday League title in 2012/13, Baffins were accepted into the HP. At the very first attempt, they won the top flight title.
After winning it for the second time in three seasons in 2015/16, the Portsmouth club sealed promotion to the Wessex League.
In their first season, they went up again - finishing runners-up with Ryan Pennery netting 39 league goals and Tyler Moret adding 28.
In their two Wessex Premier seasons so far they have finished ninth and fifth, and last season won the Wessex League Cup. They also reached the last 32 of the FA Vase, which is further than Horndean, Fareham and AFC Portchester have ever managed.
Hamble Club were members of the Wessex League in 2005/06 and 2006/07, but won just one league game in each season.
In 2012/13, they failed to complete the HPL season, their record being expunged.
But they quickly reformed, and the following season they finished runners-up in the newly-formed HPL Division 1.
A year later, they stormed to the top flight title and in 2015/16 were promoted to the Wessex in third place behind champions Baffins.
Their storming run continued when they beat Baffins to the Wessex 1 title in 2016/17 - ex-Moneyfields and Fareham striker Doug Rowe scoring 32 league goals.
Current Infinity pair Wayne Boud and Kev Cutter also turned out for Hamble Club that season.
Hamble have finished 10th and seventh in their two Wessex Premier seasons so far.
In their first season, 2017/18, Nathan Lynch won the division’s Golden Boot for hitting 35 goals in his 33 outings (and 46 in all competitions).
Lynch is still at the Monks, and has 16 goals in all competitions this term. Only Alresford’s Craig Harding (19) has more among Wessex Premier players.