It is not true to say that there is "only minimal regulation" of arbitration in the US: arbitrations are conducted under law, usually the Federal Arbitration Act but sometimes equivalent state laws and must be conducted in accordance with the rules agreed to by the parties. Further they can be appealed, however, the grounds for appeal are restricted to those enumerated in the Act or agreed by the parties.
In general, this is the case for all jurisdictions including England, however, the specific Acts that makes arbitration legal are different in each jurisdiction.
Section 69 of the UK Arbitration Act 1996 enumerates the rights of appeal and which may and may not be excluded. That said, appeals from arbitrations are rarely initiated and exen more rarely upheld. A recent decision, NYK Bulkship (Atlantic) NV v Cargill International SA  UKSC 20 has clarified this section:
The only two grounds to challenge an award which cannot be waived in an English-seated arbitration are those of substantive jurisdiction or serious irregularity. The right to appeal an award on a point of law is not a mandatory provision of the English Arbitration Act 1996.
Where this right to appeal on a point of law has not been excluded, an appeal can be brought under section 69 only with the agreement of the parties to the dispute or with the permission of the court.
Under section 69(3), the court can only grant permission if (a) the determination of the point of law will substantially affect the rights of one or more parties, (b) the question is one which the tribunal was asked to answer, (c) the arbitral award is obviously wrong or else the decision is open to serious doubt and concerns a question of general public importance, and (e) it is just and proper for the court to rule on this issue despite the parties agreeing to resolve the dispute by arbitration.
It is then at the court's discretion to confirm, vary or set aside the award or else to remit it to the tribunal in whole or in part for reconsideration in the light of their ruling. However, the statute provides that the court shall not exercise its power to set aside an award unless it is satisfied that it would be inappropriate to remit the award to the tribunal for reconsideration.
As far as I know arbitration clauses in England are not mandatory in any class of contract nor can a court order arbitration (but they can order mediation). They are restricted in employment contracts where the employee has a statutory right to appeal to an employment tribunal in that they cannot be the sole remedy and they are prohibited in insolvency proceedings and criminal matters.
Other than impartiality, there are no requirements under the Arbitration Act relating to the qualifications and characteristics of arbitrators. It is not necessary for an arbitrator to be a national of, or licensed to practice in, England.
While not strictly relevant to English law recent decisions in the USA and Canada on the unconscionably of arbitration clauses in consumer contracts (where one party can offer a "take-it-or-leave-it" contract to the other) have come to diametrically opposed conclusions. In the USA these are enforceable, in Canada they are not: probably a reflection of the different attitude of the jurisdictions on laissez-faire versus social welfare styles of capitalism although in both jurisdictions they were 5-4 decisions so more finely balanced than you might think.
I would guess that English courts would probably find the Candadian rather than the US decision more persuasive if and when the question is asked. In other common law countries, Australia is almost certainly on Canada's side particularly since for small-business contracts the standard is (since 16 November 2016) whether a term is "unfair" rather than "unconscionable".