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2 adults 1 child HH to LB 9.18am train £33.50
Buy a Network railcard for £30 that comes down to £28.55 but you can't get on till the 10.01 train
The cheapday tariff kicks in with the first train arriving in London after 10am, not leaving (in this instance) Haywards Heath. That's the 9.18am.
And it will be £26.55 (down from a full fare of £39.60) with Network Railcard. You save £13.05, which is not a bad return for your £30 investment in an annual railcard.