Without an assessment and if the OP decides to commence works, then they will be in breach of the Planning approval. Simple.
The OP could decide to vary or remove the condition, but would need to provide the LPA with sufficient evidence to back it up.
An assessment can be carried out and it may prove there is little to no risk, then happy days. The LPA would not have included the condition if they didn’t have some information to back it up.
All pre-commencement conditions are (should be) discussed with the applicant and/or agent prior to being included and issued. It would have been at that time for the applicant and/or agent to query the requirement with the LPA.
Without a suitable site investigation and/or contamination report, the OP may struggle to take out any new build warranty on the new dwelling. Even more crucial when trying to borrow money or secure a mortgage against it.
A warranty provider (i.e. NHBC) will request a complete radon protection if there is no site investigation and/or contamination report. This will also include barrier pipe.