Anglian Water states that "our requirements, which are outlined in the Build Over/Near section of the website must be considered for all works within 3 metres of the public sewer and this includes works that do not require Building Regulations approval", and that "whilst you may have obtained planning permission for your proposed works, this does not grant approval for you to build over or near to the public sewer". It publishes standard criteria for self assessment, and states that where a proposal does not comply with all of them an application is required.
The transfer on 1 October 2011 covered qualifying private sewers and lateral drains connected to the public sewer system by 1 July 2011 (gov.uk, the private sewers transfer regulations). Responsibility for an individual pipe should be checked with Anglian Water.
The Water Management Alliance states that the Land Drainage Act 1991 and each Board's Byelaws require applicants to obtain the Board's prior written consent before undertaking certain types of activities within a Board's Drainage District, and that a Board will only approve an application to discharge surface water where the watercourse can be evidenced as being connected to the wider watercourse network. Cambridgeshire County Council is the lead local flood authority, and its own page tells householders to check where rainwater will go and to consider soakaways, water butts or permeable paving.
A Fenland District Council planning committee report of 1 December 2021 for a site in the town states that "the site is located in Flood Zone 3". That is a site level statement for one address rather than a designation for the whole centre.
We would explain how you check the drainage board consent, the build over criteria and the proposed work before confirming whether permission is needed.