If a larger deposit reaches a better LTV tier, compare the marginal benefit rather than assuming more deposit is automatically best. Work out how much extra cash is tied up and what it saves in interest and fees, while preserving enough liquidity for the purchase and unexpected expenses.
There is also a trade-off between paying more deposit and retaining accessible savings. Crossing a loan-to-value boundary may reduce mortgage cost, but leaving yourself cash-poor after completion can be a worse outcome. Put a minimum cash buffer into the decision before testing larger deposits.