Well not in all cases!
In SUPPIPAT & OTHERS v NARONGDEJ & OTHERS  Costs LR 1649
Costs on amending the particulars of claim to plead foreign law: whether the costs should follow the default rule under CPR Part 17 (defendant’s costs of and occasioned by the amendment) or be costs in the case?
The starting point, as per CPR 17 PD is that a party applying for an amendment will usually be responsible for the costs of and arising from the amendment. However, that position can be departed from in an appropriate case.
This is an interesting case whereby the Claimant initially averted to the fact that there was an applicable foreign law but did not stipulate the particular foreign law, in this case Thai Law in the particulars of claim. The Defendant in its Defence raised Thai Law and coupled that by taking the stance that the Claimant could not simply plead Thai Law in their response but would have to apply to amend the particulars of claim and should therefore bear the costs of the same.
I will not go into the full detail of the judgment as it is perfectly laid out in attached link but the Court found in favour of the Claimant and allowed costs in the case.