To submit a written representation is more useful when you do not have a right of appeal, but can also be used when you do have a right of appeal. The aim of written representation is to persuade the refusing officer to reverse his decision in light of new evidence or clarification on points raised by the refusal.
Written representation will sometimes provide more documents, information or clarification on issues that the refusal may raise. The refusing officer may be pleased with the additional information and be willing to reverse his earlier decision. However, please note that in some cases, rather than further representation, a new application altogether may be advisable. Also, when you have a right of appeal, you should make sure that you do not lose your right to appeal while waiting for a response from the refusing officer.
When you have no right of appeal and you feel that the refusing officer is wrong for whatever reason, it is best to forward detailed written representation, inviting the officer to reconsider his decision. Although there is no time limit as to when you should do this, it is best to do it not more than a few days immediately after the refusal. If you are advised to re-apply, it may also be necessary to include a bit of information as to why this new application is different from the one refused, highlighting new or additional documents and information. Written representations are more successful with the Home Office than with the Embassy. You can appeal, if you have a right of appeal, and still provide written representation at the same time. This way, you will not lose your right of appeal, which must be lodged by a certain date, as the reply to the written representation may come some days after the time limit provided for you to appeal.
If your representation is not successful and you do not have a right of appeal, good lawyers in the UK may be able to "claim a right of appeal" for you. If not, perhaps Judicial Review will be the answer to your matter. As you may be aware, it is always necessary to tackle the grounds upon which you were refused, because any application you may make in the future can be refused also on the basis of the outstanding points, except the new application deals properly with the points raised in the last refusal.