The case of King v City of London Corporation [2019] EWCA Civ 2266 provides litigators with a useful clarification and warning - a Part 36 offer will not be valid if it is made "exclusive of interest". 

The case involved the claimant making a Part 36 offer of £50,000 but stated that "The offer relates to the whole of the claim for costs within the Bill and takes into account any counterclaim, but excludes interest"

In very brief summary, it was held that such an offer did not comply with CPR 36.5(4) and that "Part 36 proceeds on the basis that interest in ancillary to a claim, not a severable part of it...Interest cannot be hived off"