The Design Manual for Roads and Bridges TD 27/05 “Cross-Sections and Headrooms” gives guidance on design headroom for new bridges in Section 6. Table 6-1 (reproduced below) indicates overbridge headroom is a minimum of 5.3 m, or 5.7 m for footbridges or structures vulnerable to vehicle impact.

Overbridges $$5.30 + S$$ $$5.03 + S$$
Footbridges, sign/signal gantries and other structures vulnerable to vehicle impact $$5.70 + S$$ $$5.41 + S$$
Free standing temporary structures N/A $$5.41 + S$$
All Permanent Structures over High Load Routes $$6.45 + S$$ $$6.18 + S$$
where $$S$$ is the maximum deflection plus any construction tolerances.