Farnham were without leading wicket-taker Patrick Murphy and the in-form Chic Stedman, severely weakening their attack on a flat pitch at Roehampton.
Despite accurate spells from Peter Dickinson and Richard Norman, Bank were soon up to 60 without loss. It took the introduction of spin from both ends to force the breakthrough, as Tom Hicks dismissed Andre Jason in bizarre fashion, the ball ricocheting off Gary Clapham's gloves with the batsman's foot raised.
Farnham opted for a battle of attrition rather than out-and-out attack. Spinners Hicks and Danny Kirkland bowled the bulk of the overs and wickets fell at regular intervals.
Hicks ended with a hard-earned five-wicket haul, including a controversial bat-pad catch which caused the frustrated Stokes to kick his stumps over in disgust.
Bank continued to compile a sizeable total, however, thanks to an impressive innings by South African opener Richard Murray, who, after a reprieve early on, went on to make 117. He dispatched both spinners for huge sixes over mid-wicket and thoroughly deserved his hundred, despite another let-off in the 90s off the luckless Dickinson.
A final total of 239-8 from 60 overs was probably 20 runs too many from the Farnham point of view. Indeed, after Murray, Bank's next highest score was 27, yet Farnham can only blame themselves for some sloppy outfielding and dropped catches. Nevertheless, on a perfect batting wicket, the visitors must have fancied their chances.
The reply was hamstrung early on though, as Nick Whitworth found his stumps rearranged by the brisk Richard Pineo. Tom Hicks rode his luck early on, racing to 30, but Pineo found an extra gear and accounted for Alan Thorpe, who hooked to Mike Taylor at fine-leg.
Soon after, Hicks was trapped in front, and the visitors were left reeling as Taylor dismissed Dickinson leg before.
Farnham's batting line-up looked deep on paper, but when Clapham departed to a top edge, the 13 points looked a long way off. Then Jim Crutcher became Pineo's fourth victim.
Something of a revival followed as Richard Norman and Guy Hicks patched up the innings with patient defence and the odd well-timed boundary. But Norman's patience ran out and he was bowled round his legs attempting to sweep the leg-spin of Max Jason who also snared Robert Smith lbw.
Guy Hicks then found a partner in Kirkland and the two kept the Bank at bay until the final over, when a seemingly lifeless contest spontaneously combusted into a dramatic and, for Farnham, heart-wrenching finale.
Pineo was given one final burst and despite a shortened run-up due to an injury, the ex-Lancashire paceman removed Guy – the fourth lbw victim of the innings – with his third ball.
The unfortunate Simon Massey, promoted to the first team, attempted to cover his wicket, only for the next ball to find its way round his legs and cannon into the leg-stump. Bank were ecstatic, Farnham devastated.
Top-of-the-league Spencer visit the Park this Saturday.
Bank of England
R Murray c G Hicks b Kirkland 117
A Jason st Clapham b T Hicks 27
A Stokes c Smith b T Hicks 13
R Pineo c Clapham b Dickinson 5
T Cox c Thorpe b T Hicks 3
D Lawrence c Norman b T Hicks 14
M Taylor c G Hicks b T Hicks 8
M Jason not out 16
P Pineo run out 13
M Bird not out 1
Extras 22
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Total (for 8 wkts dec) 239
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Bowling: P Dickinson 1-37, D Kirkland 1-64, T Hicks 5-88.
Farnham
A Thorpe c Taylor b R Pineo 16
N Whitworth b R Pineo 0
T Hicks Ibw R Pineo 30
G Clapham c Lawrence b Bird 15
P Dickinson Ibw Taylor 0
R Norman b M Jason 35
J Crutcher b R Pineo 6
G Hicks Ibw R Pineo 42
R Smith Ibw M Jason 3
D Kirkland not out 8
S Massey b R Pineo 0
Extras 9
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Total 164
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Bowling: R Pineo 6-41, M Taylor 1-38, M Bird 1-24, M Jason 2-33.