No, they are not allowed to by law as stated in the official gov-docs since they are an UK-based company and the recruitment is done from there (as you stated in your question), so local laws do apply, regardless of the nationality of the applicant/candidate:
Discrimination during recruitment/Discrimination in job adverts
You must not state or imply in a job advert that you’ll discriminate against anyone. This includes saying that you are not able to cater for workers with a disability.
Only use phrases like ‘recent graduate’ or ‘highly experienced’ when these are actual requirements of the job. Otherwise you could discriminate against younger or older people who might not have had the opportunity to get qualifications.
Where you advertise might cause indirect discrimination - for example, advertising only in men’s magazines.
Questions the employer cannot ask when recruiting:
You must not ask candidates about ‘protected characteristics’ or whether they:
- are married, single or in a civil partnership
- have children or plan to have children
- Asking about health or disability
The employer can only ask about health or disability if:
- there are necessary requirements of the job that cannot be met with reasonable adjustments
- you’re finding out if someone needs help to take part in a selection test or interview
- you’re using ‘positive action’ to recruit a disabled person
"That confirms the law in UK, but I don't see how it implies that it applies to non-UK applicants and adverts?"
Answer in comments:
"It does because the company operates in the UK and therefore need to obey to UK laws. Lets imagine following scenario: In the UK it's forbidden to steal candy from your local grocery - does that law only applies to UK-residence? No - it applies for everyone stealing candy in the UK.."
In case companies are breaching employment rights in the UK, substantial penalties could be fined by the government (see reference). If that's really the case the company should replace that manager asap as stated in @Gnasher's answer before such fines could be imposed onto them.