http://www.bailii.org/ew/cases/EWHC/QB/2016/500.html

Where a Part 36 offer is accepted after the end of the relevant period, the usual costs consequences are that the claimant gets its costs up to the end of the relevant period and the offeror then gets its costs up to the date of acceptance. However, if the court considers that this position would be "unjust", it can depart from it.

Here, the defendant's offer to settle the whole claim was accepted a couple of weeks before trial and some 8 months after the end of the relevant period. The defendant argued that it would be unjust to apply the usual costs consequences because it had admitted liability for certain issues but the claimant had failed in relation to the vast majority of his pleaded claim. That argument was rejected by McKenna HHJ. He commented that: "the court's discretion to depart from the usual order is constrained by the precondition that its full enforcement would be unjust. It follows, it seems to me, that the discretion is more circumscribed than the broad discretion under CPR 44.2. Moreover, the specific considerations identified in CPR 36.17(5) have this common feature that they focus analysis on the circumstances of the making of the offer, the provision or otherwise of the relevant information in relation to it rather than more general issues as to conduct although I remind myself that the requirement to take into account all the circumstances does enable the court to take a broader view and to consider the various matters relied upon by the Defendant". 

He added that the defendant should have protected himself by making its offer in relation to only one of the pleaded issues, rather than the whole claim. Furthermore, although the claimant had been unreasonable in initially rejecting the offer and then pursuing the claim up to shortly before trial, the rules provide a remedy for that situation, in that the claimant will have to pay all the defendant's costs incurred after the end of the relevant period on the indemnity basis.