Speaking as an English lawyer, you should draw a distinction between civil and criminal cases. In civil cases settlement at any stage is encouraged. Indeed judges have a duty to suggest mediation. Settlement offers can affect costs orders as well. However, you cannot settle a criminal case, as the prosecutor is the Crown, represented by the Crown Prosecution service. The injured person is not a party to the case. There are some exceptions, for example VAT fraud, where the Defendant can agree a settlement, which is paid to the Customs authority.