is a superficially attractive but seriously flawed line of argument.
Look, I know I'm flogging a dead Archbishop here, but this is quite important: a number of his defenders are going with the line in the hope of deflecting attention from what he actually said. The current version boils down to "What's the problem with Shari'a,the Orthodox Jews do it, so you just hate Muslims, don't you?! Fascist" which demonstrates a unfortunate lack of familiarity with either English or Jewish law. Accordingly, I would like to illustrate that there are no privileges (a word which comes from prive lege, or "private law") that are available for Jews (orthodox or otherwise) that are not available to Muslims.
The various Beth Din courts have no status in English law.
I think there are two areas in which people have become confused (i) divorce and (ii) arbitration.
(i) Religious divorce clearly has nothing to do with civil divorce. However, there is a clause of the Divorce (Religious Marriage) Act 2002 which permits a husband/wife to obtain an order that the decree of divorce not be made absolute until
“[t]he parties to the marriage concerned (a) were married in accordance with (i) the usages of the Jews, or (ii) any other prescribed religious usages; and (b) must co-operate if the marriage is to be dissolved in accordance with those usages.” 
However, “(a) may be made only if the court is satisfied that in all the circumstances of the case it is just and reasonable to do so; and (b) may be revoked at any time. “.
As you can see, all though the law mentions “the Jews” specifically, it also extends to “other prescribed religious usages”. In this case it exists largely to protect a partner who gets a civil divorce but whose spouse refuses them a religious divorce [a Get in Jewish law], preventing their remarriage in an Orthodox, Conservative or Reform synagogue [rendering them an “Agunah” in Jewish law] 
The three important points to note are (i) English law  maintains supremacy (ii) the words “Get” and “Beth Din” do not appear (iii) the act AS IT STANDS contains reference to “other prescribed religious usage”. The issue is that that Shari’a courts haven’t been around as long as the Beth Din. To some extent the problem will resolve itself in time, and could be hurried along much better by someone in a civil case using the Divorce act to stop a partner from getting his/her decree nisi made absolute: This would introduce into case law one recognized Shari’a court, and we could go from there with no need to primary legislation. Alternatively, we could amend the Divorce act to say “the usages of the Jews; the usages of the Muslims; or…” ,although it seems quite unnecessary.
(ii) Arbitration. The “binding” nature of arbitration is achieved through the “Arbitration Agreement” which all parties either sign or assent to . The London Beth Din, for example, requires this, and I presume the other Beth Din do, too . It is this Agreement that makes the result of the Beth Din judgement enforceable in the civil courts . As this is a civil matter, judgements can only be pecuniary  in nature (an “Arbitration Award”). Now, this can be challenged in the courts (there is no parallel jurisdiction), and the process itself can be challenged on Natural Justice  grounds, but the assent of the parties (evidenced by the Arbitration Agreement) constitutes powerful evidence the parties were familiar with the arbitration procedures and aren’t really in a position to complain. The test, unsurprisingly given we’re talking about English Law, is that the procedure is “reasonable”.
ACAS is slightly different: set up, to provide mediation as well as arbitration, by statutory instrument (the most recent one here ). It is governed by the Arbitration Act 1996 [except a minor modification to 46(1)(b): see paragraph 5 of the SI].
As I think I’ve shown fairly conclusively, there are no special arrangements in English law that apply to Jews (Orthodox or otherwise), and not to Muslims.
Despite the best efforts of the Archbishop’s defenders, he was not calling for equality between Jews and Muslims (it clearly cannot be, as this is how the law stands at the moment). He is saying something much more dangerous.
From the speech:
I have been arguing that a defence of an unqualified secular legal monopoly in terms of the need for a universalist doctrine of human right or dignity is to misunderstand the circumstances in which that doctrine emerged, and that the essential liberating (and religiously informed) vision it represents is not imperilled by a loosening of the monopolistic framework.
He is disputing that the state has a monopoly on the law (as the defence is “not imperilled” by “loosening the monopolistic framework”), a bizarre concept: you can't really have parallel legal systems. The Political Umpire has made this point forcefully here. As PJ says in the comments:
...the really annoying thing about this whole debacle is the duplicitous pretence that he didn't say anything objectionable and controversial, and that anyone who says so has some sinister ulterior motive and/or is unable to parse such elegant and sophisticated prose.
I'm very happy to discuss the merits and demerits of having Shari'a civil courts. I'm not happy for people to tell porkies about what the ++Rowan said. God save the Archbishop from his defenders.
 Divorce (Religious Marriage) Act 2002
Inserted into the “Matrimonial Causes Act 2002” c.18
Implemented via the Family Proceeding (Amendment) Rules 2003
 Liberal and Progressive synagogues do have Beth Din, but as – I believe – they permit religious remarriage without religious divorce, the Beth Din do not issue Gets. It's also worth noting this is explicitly feminist law: it assists Agunah ("chained" women) from being screwed over by their husbands and being stopped from re-marrying.
 I can’t see any material differences between this and the amendments made to section 3A of the Divorce (Scotland) Act 1976 by the Family Law Act 2006, but as I know so little about Scottish law I’ll leave that to people who know more than I.
 However, the Beth Din have no recognition in English Law, not under these acts, nor under the Arbitration Act 1996.
 It is a requirement that the agreement be in writing, and the consent of the parties be evidenced in writing, but not actually that the parties sign it [Arbitration Act, section 5]
In the orgy of coverage that has accompanied the Archbishops speech, there has been an assumption that (i)there is only one Beth Din which (ii) constitutes some sort of monolithic institution for all Jews in the country. As I discussed in my comment above, this is false.
 Ibid., although note that the Award can only be enforced through the civil courts “with prior permission of the Beth Din”.
 Except, of course, those powers discussed in Arbitration Act 1996 paragraph 48(5) (a)-(c), but as these are in effect contact law, they need to be enforced by civil courts anyway.
 And these days, the Human Rights Act 1998, although I’m not familiar with any Human Rights case law on Beth Din.
 The Arbitration Act 1996, which you can find online at:
The ACAS Arbitration Scheme (Great Britain) Order 2004, a statutory instrument which replaced the earlier 2001 Order, which can be found at