Beccles were finally condemned to relegation from London 2NE after Saturday's defeat at Enfield.
The visitors had briefly threatened a rare success as they led 18-14 at half-time.
Beccles were 12-0 ahead after 15 minutes following tries from Marcus Sale and Stefan Holmes.
Enfield responded with a try of their own, but a couple of well taken Luke Wade penalties, allied to a conversion of the first try, extended the visitors' lead to 18-7.
The hosts then scored a converted try before half-time.
Two more tries after the break gave Ignatians the lead for the first time, before Beccles' Wade atoned for two earlier second-half misses with a successful penalty strike.
Ignatians secured the points with two further tries, before the spirited Beccles side rallied for a third try via Sam Long – but it was too late to stave off the drop.
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