Have a look at this ad:
https://www.indeed.co.uk/viewjob?jk=1f3bf4554056ad7a&l=B5+5NH&tk=1d99ofofg3d6n801&f

(cached: https://web.archive.org/web/20190425082613/https://www.indeed.co.uk/viewjob?jk=1f3bf4554056ad7a&l=B5+5NH&tk=1d99ofofg3d6n801&f)

Some of the clients are schools / educational establishments so candidates MUST be happy to go through a full DBS (no criminal record will be tolerated) and they should also have a clean UK Drivers License.

Are they allowed to use this language?

Unfortunately, there is no legal protection against this sort of discrimination, as having a criminal record is not a protected characteristic under the Equality Act 2010. To make matters worse, this is not the employer, this is a recruitment agency, who are generally intolerant towards people with a criminal record. They are happy to sign you up, to boost their numbers, but that is normally the last you'll hear from them. There speaks the voice of experience.

The DBS has a Code of Practice that all Registered Bodies are required to follow, but it just says that employers should have a written policy on the suitability of ex-offenders for employment. There is no requirement not to have a blanket ban.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

As AB2014 said, recruitment agencies are very intolerant of people with criminal records. I think it's actually good for a change that the recruiter is being upfront, at least you know where you stand so can avoid wasting any time applying.

Generally though as a rule, any work you do that will put you in contact with or working in or outside a school is best to avoid and in any case a full DBS check will be carried out.  Any sort of construction role, plumbing, carpentry, electrical etc that would place you in somewhere like a school or a high security government building (MOD or GCHQ for example) is off the menu but doesn't mean you can't work in construction, just not on those kinds of projects.

Is the blanket or otherwise general discrimination of people with convictions indirect sexual discrimination? 

The stats clearly show a disproportionate  male bias in obtaining convictions. I would hazard a guess its the same for re offending. 

Anyone ever hear this argument tested in the equality bodies? 

I think there is a small element of sexual discrimination with regards to people on the SOR convicted of underage offenses, however! the reason that individual is in that situation in the first place is because there is a victim (contact based or not) and to make it more complicated, the offense in question might not be an accurate representation of their true sexuality, since there are varying reasons why an individual commits an offense. In any case i would find it hard to believe that someone who has broken the law whereby a sexual offense has been committed can claim sexual discrimination, specifically in this country. Other countries are different with respect to their laws surrounding homosexuality for example.

The law in this country is quite tolerant of varying sexualities providing both parties are over the legal age of consent  

I have a few points to make here. First of all, you might think that GCHQ would be intolerant, but they are actually more concerned with people being vulnerable to blackmail and, of course, once they know about your record, it probably makes you a lot less vulnerable to blackmail. For most types of offence.

Whether or not it is indirect sexual discrimination is an interesting question, and good luck with getting anyone official to take it up. These days, despite all the government's assurances and empty promises and aspirations, nobody wants to be seen to be "soft on criminals". You could try the Equality and Human Rights Commission, but even if it was declared unlawful to have a blanket exclusion, those employers who wanted to get round it could do so quite easily by using a different excuse, unfortunately.

I'm not sure how sexual discrimination became sexual offending, even though I'm sure the vast majority of people on the SOR are men. Maybe we should call it gender discrimination instead.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)