I'm referring to the titles for UKHL Law Lords and UKSC Justices. Why aren't they abbreviated for brevity, when Justice is to J and Lord/Lady Justice to LJ? Eg:
"Lord" is not a judicial title: it is, and always has been a title of nobility, which it would be both a solecism and an error to abbreviate. For example, John Donaldson QC became Donaldson J, then Donaldson LJ (a Lord Justice but not a Lord), then Donaldson MR. In 1988 he was ennobled as Baron Donaldson of Lymington; only then was it correct to refer to him as Lord Donaldson.
Apparently, Supreme Court judges are not automatically ennobled; instead those who are not already Lords receive the courtesy judicial title of 'Lord', which could possibly be abbreviated to L or something similar. However, since the sole reason for creating the courtesy title was so that there should be no visible difference between the English judges and the Scottish ones who are still ennobled as a matter of course, creating a means of telling them apart seems counterproductive.
The judicial rank of English judges is abbreviated to letters after their names, but not their personal titles. High Court judges always receive a knighthood or damehood on appointment, so, to take Tim's example, John Donaldson became Sir John Donaldson on his appointment to the High Court, but in court he was Mr Justice Donaldson, abbreviated in reports or written argument to Donaldson J, and on promotion to the Court of Appeal he was Lord Justice Donaldson or Donaldson LJ. (In person in court he would have been addressed as "My Lord", and in other settings as "Sir John".)
Beyond that it becomes more complicated. For the time he was Master of the Rolls, the reports refer to him as "Sir John Donaldson, MR".
The UK Supreme Court replace the House of Lords and the highest court for the UK (leaving aside the role of the Judicial Committee of the Privy Council) in 2009. The judges in the House of Lords were full members of the House, so they were peers, in fact, since 1887 as a special type of life baron (not hereditary) known as a Lord of Appeal in Ordinary. So they were always referred to by their titles, as in the case of Lord Donaldson (barons always being referred to as "Lord" unless it is necessary to make the rank explicit); however, letters after the the were used for the Lord Chancellor, as in Lord Hailsham, LC. (There was at one time a convention that the Lord Chancellor would get a promotion to viscount, the next higher rank in the peerage, as in the case of Viscount Cave, LC.)
When the Supreme Court came into being in 2009, the existing Lords of Appeal in Ordinary became the first judges of the Supreme Court. Since they were already Lords, they were, of course, referred to by their titles. Subsequent appointments are given the courtesy title of Lord or Lady, though they are not made barons/baronesses, so they cannot sit in the House of Lords. (While the courtesy titles are comparable to the Scottish judges' titles, the immediate need was for parity between new appointments and the Lords of Appeal in Ordinary: Courtesy titles for Justices of the Supreme Court.)
The head of the Supreme Court is the President. This is abbreviated by letters after the name in the reports, so the current president (Baroness Hale of Richmond, having become a Lord of Appeal in Ordinary in 2004) is referred to as Lady Hale, P.