In reality there is usually wriggle room concerning motive or the suitability of the charge, say. But I know a lawyer who has turned away clients who have flat out confessed to him.
1) Defendants have the right to a trial, regardless of how "obviously guilty" they are in anyone's eyes.
2) Trials are, in part, about whether the state has met its burden to prove the elements of the case, regardless of the lay truth of the accused's guilt. [A]
3) Given the above, the work of a lawyer (in a trial) does not inherently involve the representation that "this defendant is innocent", but only that "there is insufficient evidence of that element of the case", which needn't be a fraud on the court, even if the prosecution's claim is true.
(With that said, more specific lies can be off limits.)
[A] A Man for All Seasons: "The world must judge according to its wits; this court must judge according to the law."
2) Yes.
3) Yes. The difficulty arises when the lawyer has been provided with evidence by the client which supports the charge.
Ultimately it's the lawyers job to present the client's case, however implausible. However, "I did it but I want to pretend I didn't" isn't a case, it's a lie.
If you agree, that's walking back on your original comment; if you disagree, that seems to go sharply against 1/2/3.
Edit: As the others note, this is going sharply against well-known legal principles. Do you have any authoritative citation that UK lawyers can't represent clients at all on a not-guilty plea while believing them to have "done it"?
But how does he know his client is guilty? Is he supposed to judge his client?
What reason would the attorney have for not believing the information that the client confesses voluntarily under the veil of attorney-client privilege?.
Considering the historical reliability of the ways in which we find people guilty of crimes that sounds like a terrible system.